A data-drivenH∞control method with dynamic performance constraints is proposed for the problem of region stabilization control in the case of unknown system matrix. By establishing a system characterization model based on measured data, the generalized pole configuration theory is ingeniously combined with the data-driven control framework. Firstly, the real-time data generated from the system operation is used to construct a data-driven dynamic characterization. A generalized pole constraint-based regional constraints condition is established to accurately regulate the state convergence rate and damping response characteristics while ensuring the stability of the closed-loop system. The classicalH∞control framework is further integrated to construct a novel data-drivenH∞performance criterion to achieve the synergistic optimization of dynamic performance constraints and disturbance suppression capability. The method gets rid of the dependence on the a priori model of the system and solves the co-optimization problem of unknown system dynamic performance regulation and robustness enhancement under a unified framework. Numerical simulations and power system control case validations show that the integrated control performance of uncertain complex systems is significantly improved.

This article addresses the variable convergence rate stability problem for nonlinear impulsive stochastic systems (NISSs). To solve the issue, a novel methodology of sliding mode surface design is presented by combining the definition of interval stability with the T-S fuzzy technique. A pioneering class of sliding mode controllers is constructed in accordance with the characteristics of the designed sliding mode surfaces and the sigmoid function. These controllers can intelligently adjust the convergence rate of the system according to practical requirements, thereby addressing the limitation of fixed convergence rate in existing results. Moreover, the proposed controllers can effectively suppress jitter and analyze the effects of different sigmoid functions on jitter suppression. Sufficient conditions are derived to ensure that the states of the NISSs reach the designed surfaces in finite time and to achieve variable convergence rate stability. The excellent performance of the proposed theoretical strategy in achieving adjustable rate convergence of the system is demonstrated through a simulation of the ball-beam system.

This article explores the$H_{\infty }$control problem based on convergence rate constraints for switched nonlinear systems under two types of asynchronous switching. First, this study investigates the variable convergence rate control issue for switched nonlinear systems. Combining the generalized pole placement idea and the Takagi–Sugeno fuzzy technique, a novel$H_{\infty }$control criterion is proposed, specifically focusing on convergence rate constraints. In addition, employing the persistent dwell-time switching to model two asynchronous scenarios in switched systems: time-delayed switching and mismatched switching, where the maximum asynchronous delay is permitted to exceed the subsystems dwell time. According to this new criterion, a novel$H_{\infty }$fuzzy controller is designed for switched nonlinear systems with asynchronous characteristics. It cannot only guarantee the asymptotic stability of the target closed-loop system but also precisely adjust the convergence rate of the system states, while also having certain anti-interference ability. Finally, numerical simulation and the tunnel diode circuit system control example prove the effectiveness of the method provided in this article.

This paper focuses on the issues of region stability/stabilization andH∞control for discrete-time impulsive Takagi-Sugeno fuzzy systems (DTIT-SFSs). Firstly, a more accurate asymptotic stability criterion is proposed by introducing the definition of region stability. It offers a more precise estimation of convergence speed and damping response for DTIT-SFSs compared to conventional stability criteria in terms of dynamic performance. Secondly, a fuzzy controller is designed based on the aforementioned region stability analysis, which can effectively control the convergence rate to the equilibrium state and ensure the desired damping response of DTIT-SFSs. Furthermore, a novelH∞fuzzy controller is designed, ensuring both a certain level ofH∞performance of DTIT-SFSs and constraint on the convergence speed and damping response of DTIT-SFSs. Finally, the functionality of this technique is validated through numerical calculations and an inverted pendulum control example

This article emphasizes the$H_{\infty }$control problem with convergence rate constraint for time-varying delay switched systems under the average dwell time switching signal. First, a novel criterion of asymptotic stability with$H_{\infty }$performance is advanced by introducing the method of average dwell time and the definition of asymptotic interval stability, which is more exact than the general stability criterion in estimating the convergence of the systems. Next, the technique of structuring$H_{\infty }$controller is derived from the stability analysis described above, which can constrain the rate of the system to equilibrium, and make it content the preset$H_{\infty }$performance. Finally, a numerical calculation and a water pollution control issue demonstrate the functionality of the technique.

This article addresses an event-triggered adaptive fuzzy tracking control problem for nonlinear systems with unknown control directions. To achieve the practical tracking, fuzzy logic systems are employed to approximate unknown nonlinear function. Nussbaum functions are adopted to address the problem of the unknown control directions. The newly designed controller not only guarantees the tracking error that converges to an arbitrary small neighborhood near the zero but also reduces the communication burden from the controller to the actuator. Moreover, the feasibility of the proposed event-triggered mechanism is verified by excluding Zeno behavior. Finally, the simulation result proves the effectiveness of the designed control scheme.

The$\mathcal {L}_{2}-\mathcal {L}_{\infty }$filter design for linear stochastic time-varying delay systems based on the filter velocity constraint is considered in this dissertation. Different from existing$\mathcal {L}_{2}\,-\,\mathcal {L}_{\infty }$performance analysis and filter design, a new criterion is proposed to make a more accurate judgment, which can not only guarantee the stability of the filtering error system with$\mathcal {L}_{2}-\mathcal {L}_{\infty }$performance level but also can estimate the convergence speed of the filter. The ideal filter should has the same convergence speed as the original system, so as to ensure the rapid convergence of the error system, but also not to reduce the anti-interference ability and increase the bandwidth of the filter system. By the new filter design method, an ideal filter can be designed, which can regulate the convergence speed of the filter system to the desired effect. A simulation instance is provided to exhibit the validity of the new approach.

This article develops a generalized$\mathcal {H}$-representation, which can transforms stochastic systems into deterministic systems. With the help of this new approach, the necessary and sufficient conditions of$p$th moment asymptotic stability and stabilization of linear stochastic systems are addressed. Meanwhile, the generalized$\mathcal {H}$-representation method is also applied to investigate$p$th moment observability and$p$th moment complete observability for the addressed systems.