In this paper, the state observer for coupled cyclic genetic regulatory networks with time delays is designed. The coupling network is composed of two cyclic genetic subnets, which inhibit each other directly. By constructing a suitable Lyapunov – Krasovskii functional velated to the eyclic struction, the delay-dependent stability criteria of the error system are investigated in the form of linear matrix inequalities. Thereby, the state observer of the considered genetic regulatory networks is obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.

This work studies the issue of global h-synchronization about high-order delayed inertial neural networks via a second-order response system (SORS) approach. Note that the h-synchronization is a flexible definition which can generalize different special synchronization types by choosing different regulation function$\hbar $. By constructing a regulation function-dependent Lyapunov–Krasovskii functional (RFD–LKF), a novel delay-dependent global h-synchronization criterion is obtained. Furthermore, an adaptive control algorithm is designed to estimate control gains online, which is useful to guarantee global h-synchronization performance as well as to decrease the control cost. And finally, the superiority of the method is verified via three numerical examples.

This article investigates the problems of state bounding description and reachable set estimation for discrete-time delayed genetic regulatory networks with bounded disturbances. A novel delay-dependent sufficient condition composing several simple linear matrix inequalities is first given to guarantee that the state trajectories converge globally exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. As applications, it is shown that these sufficient conditions are exactly global exponential stability criteria of the zero equilibrium when the disturbances vanish, and the Cartesian product of two polytopes can be viewed as a reachable set estimation of the states when the initial functions are limited into a certain range. The effectiveness of the proposed approach is illustrated by two numerical examples. Compared with the existing results, it is worthy to stress that the presented method does not need to construct any Lyapunov–Krasovskii functional and can be easily realized.

This article involves the problems of stabilization and guaranteed cost control for a class of delayed continuous-time nonlinear systems. The sufficient conditions for the existence of stabilization controllers and guaranteed cost controllers are investigated by constructing a new Lyapunov matrix-based Lyapunov–Krasovskii functional. These conditions can be easily verified by using standard compute software (e.g., the toolbox YALMIP of MATLAB), since they are expressed as simple linear matrix inequalities. Furthermore, the feasible solutions of these linear matrix inequalities are used to describe the explicit forms of stabilization controllers and guaranteed cost controllers. Finally, the validity of the proposed Lyapunov matrix-based LKF method is tested by two numerical examples.

This article studies a cooperative output-feedback secure control problem for distributed cyber-physical systems over an unreliable communication interaction, which is to achieve coordination tracking in the presence of intermittent denial-of-service (DoS) attacks. Under the switching communication network environment, first, a distributed secure control method for each subsystem is proposed via neighborhood information, which includes the local state estimator and cooperative resilient controller. Second, based on the topology-dependent Lyapunov function approach, the design conditions of secure control protocol are derived such that cooperative tracking errors are uniformly ultimately bounded. Interestingly, by exploiting the topology-allocation-dependent average dwell-time (TADADT) technique, the stability analysis of closed-loop error dynamics is presented, and the proposed coordination design conditions can relax time constraints on interaction topology switching. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

This paper investigates the exponential stability analysis issue for a class of delayed recurrent neural networks (RNNs) with semi-Markovian parameters. By constructing a stochastic Lyapunov functional and using some zoom techniques to estimate its weak infinitesimal operator, the exponential mean square stability criteria have been proposed for the Markovian neural networks with certain transition probabilities. We then generalize the homogeneous polynomial approach for the delayed Markovian RNNs with uncertain transition probabilities during the stability analysis. Theoretical results have obtained by introducing an appropriate technique for dealing with a large number of complex homogeneous polynomial matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed technique.

This paper is concerned with the exponential stability analysis of genetic regulatory networks (GRNs) with switching parameters and time delays. In this paper, a new integral inequality and an improved reciprocally convex combination inequality are considered. By using the average dwell time approach together with a novel Lyapunov-Krasovskii functional, we derived some conditions to ensure the switched GRNs with switching parameters and time delays are exponentially stable. Finally, we give two numerical examples to clarify that our derived results are effective.

This paper addresses the problem of state estimation for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms using Dirichlet boundary conditions. The nonlinear regulation function of DGRNs is assumed to exhibit the Hill form. The aim of this paper is to design a state observer to estimate the concentrations of mRNAs and proteins via available measurement techniques. By introducing novel integral terms into the Lyapunov-Krasovskii functional and by employing the Wirtinger-type integral inequality, the convex approach, Green's identity, the reciprocally convex approach, and Wirtinger's inequality, an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities (LMIs). The stability criterion depends upon the bounds of delays and their derivatives. It should be noted that if the set of LMIs is feasible, then the desired observation of DGRNs is possible, and the state estimation can be determined. Finally, two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design.

This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.

This paper deals with the problem of globally asymptotic stability for nonnegative equilibrium points of genetic regulatory networks (GRNs) with mixed delays (i.e., time-varying discrete delays and constant distributed delays). Up to now, all existing stability criteria for equilibrium points of the kind of considered GRNs are in the form of the linear matrix inequalities (LMIs). In this paper, the Brouwer's fixed point theorem is employed to obtain sufficient conditions such that the kind of GRNs under consideration here has at least one nonnegative equilibrium point. Then, by using the nonsingular M-matrix theory and the functional differential equation theory, M-matrix-based sufficient conditions are proposed to guarantee that the kind of GRNs under consideration here has a unique nonnegative equilibrium point which is globally asymptotically stable. The M-matrix-based sufficient conditions derived here are to check whether a constant matrix is a nonsingular M-matrix, which can be easily verified, as there are many equivalent statements on the nonsingular M-matrices. So, in terms of computational complexity, the M-matrix-based stability criteria established in this paper are superior to the LMI-based ones in literature. To illustrate the effectiveness of the approach proposed in this paper, several numerical examples and their simulations are given.

This paper focuses on stability analysis for a class of genetic regulatory networks with interval time-varying delays. An improved integral inequality concerning on double-integral items is first established. Then, we use the improved integral inequality to deal with the resultant double-integral items in the derivative of the involved Lyapunov-Krasovskii functional. As a result, a delay-range-dependent and delay-rate-dependent asymptotical stability criterion is established for genetic regulatory networks with differential time-varying delays. Furthermore, it is theoretically proven that the stability criterion proposed here is less conservative than the corresponding one in [Neurocomputing, 2012, 93: 19-26]. Based on the obtained result, another stability criterion is given under the case that the information of the derivatives of delays is unknown. Finally, the effectiveness of the approach proposed in this paper is illustrated by a pair of numerical examples which give the comparisons of stability criteria proposed in this paper and some literature.

In this paper, we investigate the stability of polynomial fuzzy-model-based (PFMB) control systems, aiming to relax stability conditions by considering the information of membership functions. To facilitate the stability analysis, we propose a general form of approximated membership functions, which is implemented by Taylor series expansion. Taylor series membership functions (TSMF) can be brought into stability conditions such that the relation between membership grades and system states is expressed. To further reduce the con-servativeness, different types of information are taken into account: the boundary of membership functions, the property of membership functions, and the boundary of operating domain. Stability conditions are obtained from Lyapunov stability theory by sum of squares (SOS) approach. Simulation examples demonstrate the effect of each piece of information.

We consider the problem of the robust stability of a class of uncertain T–S fuzzy neutral systems with time delay under time-varying parametric uncertainties using the Lyapunov–Krasovskii approach, where the parametric uncertainty is assumed to be norm bounded. By choosing a new Lyapunov–Krasovskii function, we are able to propose less conservative robust stability criteria in terms of linear matrix inequalities (LMIs) such that the uncertain T–S fuzzy neutral system under consideration remains asymptotically stable. The reduced conservatism of the proposed stability criterion compared with recently reported results is attributed to our using the Jensen inequality. The obtained results can also reduce the computational complexity.

This paper is concerned with the problems of D-stability and nonfragile control for a class of discrete-time descriptor Takagi-Sugeno (T-S) fuzzy systems with multiple state delays. D-stability criteria are proposed to ensure that all the poles of the descriptor T-S fuzzy system are located within a disk contained in the unit circle. Furthermore, a sufficient condition is presented such that the closed-loop system is regular, causal, and D-stable, in spite of parameter uncertainties and multiple state delays. The corresponding solvability conditions for the desired fuzzy-rule-dependent nonfragile controllers are also established. Finally, examples are given to show the effectiveness and advantages of the proposed techniques.