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T-S FUZZY MODEL AS UNIVERSAL APPROXIMATOR In this chapter, we present two results concerning the fuzzy modeling and control of nonlinear systems w1x. First, we prove that any smooth nonlinear control systems can be approximated by Takagi-Sugeno fuzzy models with linear rule consequence. Then, we prove that any smooth nonlinear state feedback controller can be approximated by the parallel distributed compensation ŽPDC. controller. Among various fuzzy modeling themes, the Takagi-Sugeno ŽT-S. model w2x has been one of the most popular modeling frameworks | Fuzzy Control Systems Design and Analysis A Linear Matrix Inequality Approach Kazuo Tanaka Hua O. Wang Copyright 2001 John Wiley Sons Inc. CHAPTER 14 ISBNs 0-471-32324-1 Hardback 0-471-22459-6 Electronic T-S FUZZY MODEL AS UNIVERSAL APPROXIMATOR In this chapter we present two results concerning the fuzzy modeling and control of nonlinear systems 1 . First we prove that any smooth nonlinear control systems can be approximated by Takagi-Sugeno fuzzy models with linear rule consequence. Then we prove that any smooth nonlinear state feedback controller can be approximated by the parallel distributed compensation PDC controller. Among various fuzzy modeling themes the Takagi-Sugeno T-S model 2 has been one of the most popular modeling frameworks. A general T-S model employs an affine model with a constant term in the consequent part for each rule. This is often referred as an affine T-S model. In this book we focus on the special type of T-S fuzzy model in which the consequent part for each rule is represented by a linear model without a constant term . We refer to this type of T-S fuzzy model as a T-S model with linear rule consequence or simply a linear T-S model. As evident throughout this book the appeal of a T-S model with linear rule consequence is that it renders itself naturally to Lyapunov based system analysis and design techniques 12 15 . A commonly held view is that a T-S model with linear rule consequence has limited capability in representing a nonlinear system in comparison with an affine T-S model 9 . In Chapter 2 the PDC controller structure was introduced 11 12 . This structure utilizes a fuzzy state feedback controller which mirrors the structure of the associated T-S model with linear rule consequence. As shown throughout this book T-S models together with PDC controllers form a powerful framework for fuzzy control systems resulting in many successful applications 10 13 14 . 277 278 T-S FUZZY MODEL AS UNIVERSAL APPROXIMATOR In this chapter we attempt

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