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Qunxian Zheng,Hongbin Zhang,Dianhao Zheng 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.3
The stability analysis and asynchronous stabilization problems for a class of discrete-time switchednonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzymodel is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems aremodeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions(FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for theopen-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions forthe closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results andasynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numericalexamples are provided to illustrate the effectiveness of the results obtained.
Robust H∞ and Guaranteed Cost Filtering for T-S Fuzzy Systems with Multipath Quantizations
Qunxian Zheng,Wei Shi,Ke Wu,Shengquan Jiang 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.2
This paper investigates the problems of robust H∞ and guaranteed cost filtering for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy systems with multipath quantizations. The “multipath quantizations” mean that both the measurement output and estimated output of the uncertain T-S fuzzy systems are quantized by two different dynamic quantizers before they are transmitted. The unknown uncertain parameters are assumed to be norm bounded. Through applying the S-procedure and introducing some slack matrix variables, new sufficient conditions about the robust asymptotical stability with specific performance measures for quantized filtering error system have been developed via the fuzzy-basis-dependent Lyapunov function approach. The desired robust H∞ filter, robust guaranteed cost filter and dynamic quantizer parameters can be easily obtained by means of linear matrix inequalities (LMIs). Finally, a practical example about the mass-spring-damper mechanical system is given.
Dynamic Event-triggered Quantitative Feedback Control for Switched Affine Systems
Xiang Lu,Hongyu Sun,Xinzheng Lyu,Anhao Wen,Yinjing Guo,Gang Jing,Qunxian Zheng 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.6
This paper focuses on the design of a dynamic output feedback controller for switched affine systems under limited communication resources. Since the system states information is difficult to obtain, the dynamic output feedback switching function is considered to stabilize the switched affine system. Quantized output measurements are transmitted to the dynamic output feedback controller to reduce the communication load. In order to significantly reduce the sampling frequency, an event-triggering mechanism is introduced to detect the event periodically. By using Lyapunov stability theory and linear matrix inequality (LMI) technique, a set of dynamic output feedback gains together with a switching rule are designed assuring the global asymptotic stability of the desired equilibrium point. More specifically, the design conditions do not require that there exist a stable convex combination of the subsystems state-space matrix. Finally, a numerical example show the validity of the obtained results of this paper.
A Novel Approach to H2 and H∞ Filter Design for Discrete-time Switched Affine Systems
Zhenting Fu,Xiaozeng Xu,Xinyue Yang,Hongbin Zhang,Qunxian Zheng 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.6
This paper focuses on solving H2 and H∞ filtering problems for discrete-time switched affine systems. By constructing a discrete-time affine filtering error system, an observer-based filter and its corresponding switching function can be obtained by solving the linear matrix inequalities. For discrete-time switched affine systems, the performance indexes of the system in this neighborhood cannot be analyzed due to the existence of affine terms. The technique proposed in this note leads the system’s trajectory to the limit cycle so that the resulting conditions can consider the weighted H2 and H∞ performance level of the system. In addition, it is proved that the H2 and H∞ guaranteed cost is upper bounded and the upper boundaries are formulated by solving an optimization problem. Finally, two numerical examples are given to verify the theory.