Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and H∞ Performance Conditions
ABSTRACT In this paper, new approaches to Hinfin controller design for a class of discrete-time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, two relaxed conditions of nonquadratic stability with H infin norm bound are presented for this class of systems. The two relaxed conditions are shown to be useful in designing fuzzy control systems. By introducing some additional instrumental matrix variables, the two relaxed conditions are used to develop Hinfin controllers. In the control design, the first relaxed condition has fewer inequality constraints, but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables. Finally, two examples are given to demonstrate the applicability of the proposed approach
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ABSTRACT: Based on a Takagi–Sugeno (T–S) fuzzy model and an inverse system method, this paper deals with the problem of actuator fault estimation for a class of nonlinear dynamic systems. Two different estimation strategies are developed. Firstly, T–S fuzzy models are used to describe nonlinear dynamic systems with an actuator fault. Then, a robust sliding mode observer is designed based on a T–S fuzzy model, and an inverse system method is used to estimate the actuator fault. Next, the second fault estimation strategy is developed. Compared with some existing techniques, such as adaptive and sliding mode methods, the one presented in this paper is easier to be implemented in practice. Finally, two numerical examples are given to demonstrate the efficiency of the proposed techniques.International Journal of Applied Mathematics and Computer Science 01/2012; 22(1). · 1.01 Impact Factor
Conference Paper: Observer-based H ∞ control for discrete-time T-S fuzzy systems[Show abstract] [Hide abstract]
ABSTRACT: This paper is concerned with the problem of observer-based H∞ control for discrete-time Takagi-Sugeno (T-S) fuzzy systems, and new design methods are presented. By defining a fuzzy Lyapunov function, a new sufficient condition guaranteeing the H∞ performance of the T-S fuzzy systems is derived, and the condition is expressed by a set of linear matrix inequalities (LMIs). In comparison with the existing literature, the proposed approach may provide more relaxed condition while ensuring better H∞ performance. The simulation results illustrate the effectiveness of the proposed approach.Proceedings of the 21st annual international conference on Chinese control and decision conference; 06/2009
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ABSTRACT: In this article we consider the synthesis of dynamic output feedback compensators for linear discrete-time parameter-varying systems. By assuming that the time-varying parameters can be measured or estimated in real-time, two full-order compensators are considered: one that is partially dependent on the parameters and other that is totally dependent. Closed-loop stability and time performance are verified via a parameter dependent Lyapunov function. LMI conditions are given for the synthesis of the controllers. To cope with practical applications, particularly in the case where the time-varying linear model represents locally the dynamics of a nonlinear plant, additional conditions are also considered to take into account the local validity of the model. The proposed results are applied to a nonlinear system that is locally represented by a Takagi-Sugeno fuzzy model.Sba Controle & Automação Sociedade Brasileira de Automatica 10/2012; 23(5):517-529.