Discrete polynomial fuzzy systems control. Issue 4 (1st March 2014) - Chen, Ying‐Jen; Tanaka, Motoyasu; Tanaka, Kazuo; Ohtake, Hiroshi; Wang, Hua O.
Abstract : This study presents a sum‐of‐squares (SOS) approach to stable control and guaranteed cost control of discrete polynomial fuzzy systems. The SOS framework presented in this paper offers a new paradigm over the existing linear matrix inequality (LMI) approaches to discrete Takagi–Sugeno (T–S) fuzzy models. At first, this study, newly introduces a discrete polynomial fuzzy model that is more general and effective than the well‐known discrete T–S fuzzy model. With considering the operating domain, stable control design conditions are then derived based on state‐dependent Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this study could be more general than the LMI design approaches based on quadratic Lyapunov functions. Moreover, this study also discusses a guaranteed cost control design which is carried out by minimising the upper bound of a given performance function. All the design conditions derived in this study can be represented in terms of SOS and are symbolically and numerically solved via the SOSOPT and the SeDuMi, respectively. Finally, the ball‐and‐beam system is provided as an example to illustrate the utility of the proposed SOS‐based design approach.