If a control input signal constructed by backstepping is used to generate an event-triggered control signal, then not only the real control input is discontinuous, but all the virtual control signals that make up the control signal are also discontinuous and have the same triggering instants with the control input. This fact makes the control design and stability analysis more difficult and complex via backstepping. This article focuses on this problem and works at coming up a new backstepping design procedure of event-triggered fuzzy adaptive control for nonlinear strict feedback systems. A concurrent event-triggered mechanism is proposed to ensure that the real control input and the virtual control signals have the same triggering instants. Then, a systemic backstepping design procedure is developed to construct event-triggered fuzzy adaptive controller. The Lyapunov technique for nonlinear impulsive system is employed to provide the closed-loop stability analysis. It is shown that the derived event-triggered fuzzy adaptive controller ensures that the closed-loop system output well follows the desired tracking trajectory and the other closed-loop signals remain bounded. Eventually, two examples are provided to further verify the applicability and reliability of the presented control scheme.

This article aims at this problem of adaptive neural tracking control for state-constrained systems. A general fixed-time stability criterion is first presented, by which an adaptive neural control algorithm is developed. Under the action of the proposed adaptive neural tracking controller, the tracking error converges into a small neighborhood around the origin in fixed time; meanwhile, all system states abide by the corresponding state constraints for all the time. The main difference between the present research and the previous control schemes for state-constrained systems is that this article proposes a novel and feasible approach to ensure that the constructed virtual control signals satisfy the state constraints on the corresponding states viewed as the virtual control inputs. Such an approach guarantees theoretically that all the system states cannot violate their constrained requirements at any time. Finally, two simulation examples provide support to the proposed results.

This article addresses the finite-time consensus tracking control problem for nonlinear multiagent systems (MASs), in which state variables are unmeasured and nonlinear functions are totally unknown. An observer is designed to estimate state variables and fuzzy-logic systems are employed to approximate nonlinearities. Then, an observer-based adaptive fuzzy consensus tracking controller is developed by using the backstepping technique and constructing a novel barrier Lyapunov function with the consideration of the characteristics of MASs. The proposed control protocol can guarantee that: 1) all signals in the closed-loop system keep bounded and 2) the consensus tracking error converges to a prespecified region of the origin in the prescribed finite time. Compared with the existing observer-based finite/fixed-time control protocols, the settling time and the convergence region in our work can be both preassigned by the designer and not affected by the unknown positive constant, which lies in the Lyapunov derivative inequality. Finally, two comparison simulation examples, including a numerical example and a practical example, check the availability of the designed control scheme.

This article studies the stability and stabilization of Takagi–Sugeno (T–S) fuzzy time-delay systems under sampled-data control via a new asymmetric Lyapunov–Krasovskii functional (LKF) method. The method improves the common symmetric basic functional term. Besides, we improve the looped-functional term and the discontinuous functional term through combining the integral about time delay and each sampling interval, respectively. Based on the abovementioned new approaches, we present the stability and stabilization results with less conservativeness than the literature through linear matrix inequalities. In the process, we introduce a simplification approach for stabilization of sampled-data control, which effectively reduces the computational complexity of results. At last, we provide three examples to verify the effects and advantages of our results.

This article presents a new asymmetric Lyapunov–Krasovskii functional method on the stability and stabilization of Takagi–Sugeno fuzzy systems with time delay. For the reduction of conservativeness, combining the method with the membership-function-dependent approach, we propose a novel delay-dependent stability condition in the form of linear matrix inequalities. Based on the condition, we further obtain a novel condition of stabilization. At the end, we provide two numerical examples to verify the advantage of the stability and stabilization approaches, respectively.

This article discusses the consensus tracking issue for multiagent systems, and the purpose is to develop a fixed-time consensus proposal by fuzzy adaptive method. To this end, we first set up a more general fixed-time stability criterion. By using the proposed stability criterion, a backstepping design procedure is presented to construct the fixed-time fuzzy adaptive controller. The suggested fuzzy adaptive control protocol guarantees that 1) for each agent, its closed-loop signals keep bounded; 2) the consensus tracking error tends to a small region around origin in fixed time. In addition, the virtual control signals are constructed to be the piecewise functions to prevent the singularity of their derivatives. Curve fitting method is used such that the designed virtual control signals are derivable at the point of partition. Finally, numerical simulation further checks the validity of the suggested control strategy.

The purpose of this article is to present a novel backstepping-based adaptive neural tracking control design procedure for nonlinear systems with time-varying state constraints. The designed adaptive neural tracking controller is expected to have the following characters: under its action: 1) the designed virtual control signals meet the constraints on the corresponding virtual control states in order to realize the backstepping design ideal and 2) the output tracking error tends to a sufficiently small neighborhood of the origin with the prescribed finite time and accuracy level. By combining the barrier Lyapunov function approach with the adaptive neural backstepping technique, a novel adaptive neural tracking controller is proposed. It is shown that the constructed controller makes sure that the output tracking error converges to a small neighborhood of the origin with the prespecified tracking accuracy and settling time. Finally, the proposed control scheme is further tested by simulation examples.

This article is aimed at developing a finite-time adaptive fuzzy control strategy for a class of nonlinear strict-feedback systems. For the first time, a fast finite-time practical stability criteria is set up, which provides an effective approach to address the finite-time adaptive fuzzy control design. Furthermore, a systematic finite-time adaptive fuzzy control design procedure is developed by embedding that practical stability criteria. The closed-loop stability analysis shows that the tracking error converges to a small region around the origin in finite time. Meanwhile, all the signals in the closed-loop system are bounded. At last, the presented results are tested by a numerical example.

This paper addresses adaptive neural output feedback control for uncertain nonlinear switched systems. The main difficulty for control design comes from the loss of the precise information on those virtual coefficients of each subsystem. To overcome this difficulty, we give a robust observer design scheme by using convex combination approach. Furthermore, develop an observer-based output feedback control strategy. During the procedure of control design, adaptive neural control approach is used to deal with the unknown nonlinear functions and backstepping technique is employed to construct the ideal control laws. It is shown that the presented control law achieves the control issue of getting small tracking error, meanwhile, ensuring boundedness of all the closed-loop signals. Finally, a simulation example is used to test our results.

This paper studies the finite-time stabilization of a class of stochastic nonlinear systems. Different from functions which are necessarily known in the conventional finite-time control of nonlinear systems, the nonlinear functions can be completely unknown in this paper. By applying fuzzy-logic systems to approximate the unknown nonlinearities, a novel adaptive finite-time control strategy is proposed. However, due to the existence of approximation errors, the existing finite-time stability criterion cannot be used to analyze the stability of stochastic nonlinear systems. To deal with this difficulty, a finite-time stability criterion, by utilizing the mean value theorem of integrals, is first established in Lemma 5, which plays a significant role in the finite-time stability analysis of stochastic nonlinear systems. Then, the finite-time mean square stability of a stochastic nonlinear system is proved by combining Lemma 3 with Jensen's inequality.

This article studies the problem of the fuzzy H∞filter design for nonlinear networked control systems through eventtriggered communication (ETC) scheme. First, a novel adaptive ETC scheme is given to determine whether the sampled measurement output should be released to communication network or not. Consequently, less communication resources are occupied under the desired H∞performance. Second, augmented fuzzy lineintegral Lyapunov function is introduced in the H∞performance analysis of filter error systems, such that the information of time derivative of membership functions are fully considered to reduce the conservativeness of networked fuzzy filter design. Different from the existing results, the upper bounds of time derivative of membership functions need not to be known prior. Third, the resulting filter error system is modeled as time-delay system under ETC mechanism and asynchronous premise in a unified framework. As a result, applying Lyapunov theory and inequality technique, new sufficient condition is obtained to meet the H∞performance for the filter error systems. Further, the corresponding filter and event-triggering parameters are codesigned and solved by a set of linear matrix inequalities. Finally, two examples are offered to demonstrate the advantage of the proposed method.

This paper aims to address adaptive tracking control problem of distributed multiagent systems. Differing from some existing works, each follower under consideration is modeled by a nonlinear nonstrict feedback system, especially, the virtual and real control gains are unknown functions rather than constants. To overcome the difficulty caused by the unknown nonlinearities, radial basis function neural networks are employed to model those unknown nonlinearities. Then, adaptive neural approach and backstepping technique are combined to construct the consensus tracking control protocol. It is shown that under the action of the suggested control protocol, whole closed-loop system is stable and all the outputs of followers ultimately track the reference signal, i.e., the output of the leader, synchronously. Numerical simulation is presented to further demonstrate the efficacy of the suggested control proposal.

This paper is concerned with the regularization and stabilization problems for rectangular discrete-time fuzzy systems with time delay. A dynamic compensation is designed to ensure that the close-loop system is square, and a necessary and sufficient condition is proposed to guarantee the existence of a dynamic compensation with which the close-loop system is regular and causal. Moreover, sufficient conditions are derived in terms of bilinear matrix inequalities to guarantee the admissibility of the closed-loop system. We present an efficient algorithm which is proved to be convergent to solve the conditions. Two examples are given to show the effectiveness and efficiency of the proposed method.

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.

This paper addresses the finite-time tracking issue for nonlinear quantized systems with unmeasurable states. Compared with the existing researches, the finite-time quantized feedback control is considered for the first time. By proposing a new finite-time stability criterion and designing a state observer, a novel adaptive neural output-feedback control strategy is raised by backstepping technique. Under the presented control scheme, the finite-time quantized feedback control problem is coped with without limiting assumption for nonlinear functions.

This paper considers the problems of designing a robust observer and developing a backstepping-based adaptive fuzzy control scheme for a class of strict-feedback systems, in which the virtual control coefficients are unknown. By using convex combination method, a robust fuzzy observer has been constructed to estimate the unmeasurable system state variables. Further, an observer-based adaptive fuzzy control scheme has been proposed. During the controller design procedure, fuzzy logic systems are used to model the unknown nonlinear functions, adaptive technique and backstepping are combined to construct the ideal virtual and the real laws. The proposed adaptive fuzzy output feedback controller guarantees that the tracking error converges to a small neighborhood of the origin and all the signals in the adaptive closed-loop system are bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

This paper addresses the problem of adaptive neural tracking control for nonlinear nonstrict-feedback systems. The state variables are immeasurable and only the system output is available. A neural observer is constructed to estimate these unknown system state variables. An observer-based adaptive neural tracking control scheme is developed via backstepping approach. It is shown that the designed controller guarantees that the system output well follows the desired reference signal, and meanwhile, other closed-loop signals remain bounded. Finally, two simulation examples are used to test our results.

This paper studies the problems of stability analysis and stabilization for a class of nonlinear systems represented by T-S fuzzy models with time-varying delay. Based on a reinforced Lyapunov-Krasovskii functional, a new delay-dependent criterion for ensuring the asymptotic stability of the concerned fuzzy systems has been derived in terms of linear matrix inequalities (LMI). Then, the state feedback control design is derived to achieve the stabilization. The efficiency and merits of the proposed approach are shown through several numerical examples.

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

This paper focuses on backstepping-based adaptive neural control for switched nonlinear systems in nonstrict-feedback form. A structural characteristic of radial basis function neural networks is first developed. With this structural characteristic, adaptive neural backstepping has been extended to the switched nonlinear systems with nonstrict-feedback structure. By using a common Lyapunov function method, an adaptive neural controller is constructed by backstepping technique. It is shown that under the action of the suggested controller, all the closed-loop signals are bounded and meanwhile the system output follows the desired reference signal well. Finally, a numerical simulation example is used to illustrate the effectiveness of our results.

This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict-feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first proposed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficulties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approximation capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach.

This paper considers the problem of observer-based adaptive fuzzy control for a class of nonlinear time-delay systems in nonstrict-feedback form, which includes the nonlinear strict-feedback systems as a special case. An adaptive fuzzy output feedback backstepping approach is first proposed for nonlinear systems in nonstrict-feedback form. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Adaptive technique and backstepping are utilized to construct a controller. The proposed adaptive fuzzy output feedback controller guarantees that all the signals in the adaptive closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

In this paper, we consider the problem of observer-based adaptive neural output-feedback control for a class of stochastic nonlinear systems with nonstrict-feedback structure. To overcome the design difficulty from the nonstrict-feedback structure, a variable separation approach is introduced by using the monotonically increasing property of system bounding functions. On the basis of the state observer, and by combining the adaptive backstepping technique with radial basis function neural networks' universal approximation capability, an adaptive neural output feedback control algorithm is presented. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in the sense of mean quartic value. Simulation results are provided to show the effectiveness of the proposed control scheme.

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

In this paper, the problem of H∞ filter design for nonlinear interconnected systems with time-varying delays through Takagi-Sugeno fuzzy models is revisited. Based on the fuzzy line-integral Lyapunov function approach and the reciprocally convex inequality, a delay-dependent decentralized H∞ filter is designed by guaranteeing the asymptotic stability and a prescribed H∞ performance index for the overall filter error system. A new sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities. The present method provides improvements and produces better results than existing ones in the literature. Two examples are given to show the advantages and effectiveness of the proposed results.

This brief considers the problem of neural networks (NNs)-based adaptive dynamic surface control (DSC) for permanent magnet synchronous motors (PMSMs) with parameter uncertainties and load torque disturbance. First, NNs are used to approximate the unknown and nonlinear functions of PMSM drive system and a novel adaptive DSC is constructed to avoid the explosion of complexity in the backstepping design. Next, under the proposed adaptive neural DSC, the number of adaptive parameters required is reduced to only one, and the designed neural controllers structure is much simpler than some existing results in literature, which can guarantee that the tracking error converges to a small neighborhood of the origin. Then, simulations are given to illustrate the effectiveness and potential of the new design technique.

This paper focuses on approximation-based adaptive neural control of a class of nonlinear non-strict-feedback systems. Based on the structural characteristic and the monotonously increasing property of the system bounding functions, a variable separation method is first developed. By this method, an approximation-based adaptive backstepping approach is proposed for a class of nonlinear non-strict-feedback systems. It is shown that the proposed controller guarantees semi-global boundedness of all the signals in the closed-loop systems. Three examples are used to illustrate the effectiveness of the proposed approach.

This paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict-feedback form. A new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead-zone nonlinearity. Control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems. The proposed adaptive fuzzy controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples illustrate the effectiveness of the proposed approach.

This paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict-feedback form with unknown backlash-like hysteresis nonlinearities. To overcome the design difficulty of nonstrict-feedback structure, variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic. By combining radial basis function neural networks' universal approximation capability with an adaptive backstepping technique, an adaptive neural control algorithm is proposed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are four-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results further show the effectiveness of the presented control scheme.

The stability problem for delayed complex-valued recurrent neural networks is considered in this paper. By separating complex-valued neural networks into real and imaginary parts, forming an equivalent real-valued system, and constructing appropriate Lyapunov functional, a sufficient condition to ascertain the existence, uniqueness, and globally asymptotical stability of the equilibrium point of complex-valued systems is provided in terms of linear matrix inequality. Meanwhile, the errors in the recent work are pointed out, and even if the result therein is correct, it is shown that our result not only improves but also generalizes in that work. Numerical examples are given to show the effectiveness and merits of the present result.

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with input saturation. To overcome the design difficulty from nondifferential saturation nonlinearity, a smooth nonlinear function of the control input signal is first introduced to approximate the saturation function; then, an adaptive fuzzy tracking controller based on the mean-value theorem is constructed by using backstepping technique. The proposed adaptive fuzzy controller guarantees that all signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighborhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.

In this paper, an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict-feedback systems without the requirement of states measurement. The stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties (unknown nonlinear functions) and, in the presence of unmodeled dynamics, dynamics disturbances. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique with the stochastic small-gain approach, a new adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance. In addition, the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties.

This paper is concerned with the synchronization problems for an array of neural networks with hybrid coupling and interval time-varying delay. First, a novel augmented Lyapunov-Krasovskii functional (LKF) method is proposed to develop delay-dependent synchronization criteria for the networks, which makes use of more relaxed conditions by employing the new type of augmented matrices with Kronecker product operation. The proposed method can handle a multitude of Kronecker product operations in the LKF and alleviates the requirements of the positive definiteness of some conditional matrices which are usually considered in the existing methods for complex networks. This leads to a significant improvement in the performance of the synchronization criteria, i.e., less conservative synchronization results can be obtained. Meanwhile, the case of fast time-varying delay can also be handled by the proposed method. Furthermore, based on the derived criteria, a robust synchronization criterion is obtained for the system with uncertainties both in coefficient and coupling matrix terms. Since an expression based on linear matrix inequality is used, the proposed criteria can be easily checked in practice. Finally, numerical examples are provided to show the effectiveness of the proposed method.

Controlling nonstrict-feedback nonlinear systems is a challenging problem in control theory. In this paper, we consider adaptive fuzzy control for a class of nonlinear systems with nonstrict-feedback structure by using fuzzy logic systems. A variable separation approach is developed to overcome the difficulty from the nonstrict-feedback structure. Furthermore, based on fuzzy approximation and backstepping techniques, a state feedback adaptive fuzzy tracking controller is proposed, which guarantees that all of the signals in the closed-loop system are bounded, while the tracking error converges to a small neighborhood of the origin. Simulation studies are included to demonstrate the effectiveness of our results.

This paper focuses on the problem of adaptive control for a class of nonlinear time-delay systems with unknown nonlinearities and strict-feedback structure. Based on the Lyapunov-Krasovskii functional approach, a state-feedback adaptive controller is constructed by backstepping. The proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal, and all the signals of the closed-loop system remain bounded. Compared with the results that exist, the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy-membership functions; therefore, a priori knowledge of fuzzy approximators is not necessary for control design, and the proposed approach requires only one adaptive law for an nth-order system. Two numerical examples are used to illustrate the effectiveness of the proposed approach.

"For original paper see Y. S. Yang, C. J. Zhou, ibid., vol. 13, no. 1, p. 104-114, (2005)". In this note, we point out some mistakes in a 2005 paper by Yang and Zhou.

This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.

This paper discusses the stabilization of Takagi-Sugeno (T-S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T-S fuzzy input delay systems without uncertainties. A separate design principle is developed. Some illustrative examples are given to show the effectiveness and the feasibility of the proposed methods.

This paper is concerned with the$H_{\infty} $filter design for nonlinear systems with time-varying delay via Takagi–Sugeno fuzzy model approach. Delay-dependent design method is proposed in terms of linear matrix inequalities (LMIs), which forms the main contribution of this paper. The main technique used is the free-weighting matrix method combined with a matrix decoupling approach. The results for rate-independent case, delay-independent case, and delay-free case are also given as easy corollaries. An illustrative example is given to show the effectiveness of the present method.

This paper proposes a novel adaptive neural control scheme for a class of perturbed strict-feedback nonlinear time-delay systems with unknown virtual control coefficients. Based on the radial basis function neural network online approximation capability, an adaptive neural controller is presented by combining the backstepping approach and Lyapunov-Krasovskii functionals. The proposed controller guarantees the semiglobal boundedness of all the signals in the closed-loop system and contains minimal learning parameters. Finally, three simulation examples are given to demonstrate the effectiveness and applicability of the proposed scheme.

In this paper, the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with the block-triangular structure. The fuzzy logic systems are used to approximate the unknown nonlinear functions. By using the backstepping technique, the adaptive fuzzy tracking control design scheme is developed, which has minimal learning parameterizations. The adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Two examples are used to show the effectiveness of the approach

This correspondence studies the problem of observer-based H infinity control for time-delay Takagi-Sugeno (T-S) fuzzy systems. It provides a delay-dependent linear matrix inequality (LMI)-based method for the control design. It is known that the key important problem in the literature, even for delay-independent case, lies in the difficulty of decoupling matrix variables in corresponding matrix inequalities. This correspondence suggests a decoupling technique for solving matrix inequalities with coupled variables, and provides an LMI-based algorithm by adopting the idea of the cone complementarity problem. The derivation relies on the appropriate choice of Lyaponuv-Krasovskii functionals which incorporate the intersections among local systems. Illustrative examples are given to show the effectiveness of the present delay-dependent result.

Fuzzy approximate disturbance decoupling concept is introduced for a class of multiple-input-multiple-output (MIMO) nonlinear systems with completely unknown nonlinearities. Based on backstepping technique, a fuzzy almost disturbance decoupling control scheme is proposed. The fuzzy controllers guarantee internal uniform ultimate boundedness of the closed-loop adaptive systems and render a bounded approximate L/sub 2/ gain from the disturbance input to the output. The developed design scheme is applied to control a two continuous stirred tank reactor process. The simulation results illustrate the effectiveness of the method proposed in this paper.

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.