Stability Analysis And Controller Design For Fuzzy Systems

The strategy of fuzzy control is one of the intelligent control scheme, which is based on the concept of "fuzzy sets" proposed in 1965 by Prof. Zadeh L A in American. The research of fuzzy control theory includes a series of main problems, such as the stability and robustness analysis, the system design approach and the improvement of the system performance etc. In 1985, Takagi T and Sugeno M proposed the Takagi-Sugeno (T-S) fuzzy model, which brings far-researching impact on fuzzy control theory and its application, and makes the stability analysis of fuzzy systems to a new theoretical height. An advantage of T-S fuzzy model is that it can fully use Lyapunov stability theory to analyze stability of systems and design controller,and a systematic method is provided to study the problem of stability of nonlinear systems and controller design by T-S fuzzy modelling for nonlinear systems.Combining with the Lyapunov stability theory, robust control theory and H∞control theory, using the Linear Matrix Inequality (LMIs), this thesis discussed the stability and stabilization problems of fuzzy systems based on T-S linear model and T-S bilinear model in detail, respectively.The main research works in this thesis can be described as follows:1. For the conservation of checking the robust stability of uncertain discerte fuzzy system with the approaches those have been proposed,sufficient conditions for globally asymptotical H-infinity stability of uncertain discrete T-S fuzzy system are presented by using fuzzy Lyapunov function.State-feedback controller is designed by the method of parallel distributed compensation (PDC). The controller design involves solving a set of LMIs by introducing multiply additional matrix variables.2. A new method for the delay-dependent stability analysis for continuous-time Takagi and Sugeno(T-S) fuzzy systems with a time-varying delay is suggested, which is less conservative than other existing ones.First, based on a fuzzy Lyapunov-Krasovskii functional (LKF), a delay-dependent stability criterion is derived for the fuzzy systems.In the derivation process, some free-weighting matrices are introduced to expressed the relationships among the terms of the systems equation, and among the terms in the Leibuiz-Newton formula, which may avoid the conservation producing by some bounding inequalities for cross products between two vectors and model transformation. At the same time, the subtle difference is payed careful attention to, which is largely ignored in the existing literature.3. A delay-dependent robust H∞non-fragile control problem is presented for a class of uncertain T-S fuzzy systems with time-varying delay. A delay-dependent robust non-fragile controller is designed via a fuzzy Lyapunov-Krasovkii functional and the PDC approach, such that the closed-loop systems are robust asymptotically stable in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such robust non-fragile controller is drived via the LMI. The feedback controller design involves solving a set of linear matrix inequalities (LMIs).4. The problem of decentralized state feedback control is presented for a nonlinear interconnected system with time-varying delay in both states and inputs which is composed by a number of T-S fuzzy bilinear subsystems with interconnections. Based on the Lyapunov criterion and the parallel distribute compensation scheme, the delay-dependent stabilization sufficient conditions are derived for the whole close-loop fuzzy interconnected systems. The corresponding decentralized fuzzy controller design is converted into a convex optimization problem with LMI constraints.5. The problem of decentralized static output feedback control is presented for a nonlinear interconnected system which is composed by a number of T-S fuzzy bilinear subsystems with interconnections. Based on the Lyapunov criterion, some sufficient stabilization conditions are derived for the whole close-loop fuzzy interconnected systems. The stabilization conditions are further formulated into LMIs so that the corresponding decentralized controllers can be easily obtained by using the Matlab LMI toolbox.Finally, some concluding remarks are given and the future research works are pointed out.