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LMI CONTROL PERFORMANCE CONDITIONS AND DESIGNS The preceding chapter introduced the concept and basic procedure of parallel distributed compensation and LMI-based designs. The goal of this chapter is to present the details of analysis and design via LMIs. This chapter forms a basic and important component of this book. To this end, it will be shown that various kinds of control performance specifications can be represented in terms of LMIs. | Fuzzy Control Systems Design and Analysis A Linear Matrix Inequality Approach Kazuo Tanaka Hua O. Wang Copyright 2001 John Wiley Sons Inc. CHAPTERS ISBNs 0-471-32324-1 Hardback 0-471-22459-6 Electronic LMI CONTROL PERFORMANCE CONDITIONS AND DESIGNS The preceding chapter introduced the concept and basic procedure of parallel distributed compensation and LMI-based designs. The goal of this chapter is to present the details of analysis and design via LMIs. This chapter forms a basic and important component of this book. To this end it will be shown that various kinds of control performance specifications can be represented in terms of LMIs. The control performance specifications include stability conditions relaxed stability conditions decay rate conditions constrains on control input and output and disturbance rejection for both continuous and discrete fuzzy control systems 1 -3 . Other more advanced control performance considerations utilizing LMI conditions will be presented in later chapters. STABILITY CONDITIONS In the 1990 s the issue of stability of fuzzy control systems has been investigated extensively in the framework of nonlinear system stability 1 -18 . Today there exist a large number of papers on stability analysis of fuzzy control in the literature. This section discusses some basic results on the stability of fuzzy control systems. In the following Theorems 5 and 6 deal with stability conditions for the open-loop systems. Theorem 5 can be readily obtained via Lyapunov stability theory. The proof of Theorem 6 is given in 4 7 . 49 50 LMI CONTROL PERFORMANCE CONDITIONS AND DESIGNS THEOREM 5 CFS The equilibrium of the continuous fuzzy system with u t 0 is globally asymptotically stable if there exists a common positive definite matrix P such that ATP PA i 0 i 1 2 . r that is a common P has to exist for all subsystems. THEOREM 6 DFS The equilibrium of the discrete fuzzy system with u t 0 is globally asymptotically stable if there exists a .

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