Stability analysis and systematic design of Takagi–Sugeno fuzzy control systems

Abstract

The stability analysis and systematic design techniques of Takagi–Sugeno (T–S) fuzzy control systems are discussed in this paper. In order to make good use of the structural information in rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition of the input variables of fuzzy control systems is well defined. Based on the property analysis of fuzzy control systems with SFP inputs, the stability of both the input-free T–S fuzzy systems and the closed-loop T–S fuzzy control systems are studied in detail with the extended Lyapunov theory, and two theorems to check the stability of T–S fuzzy control systems are proposed. These methods, which only require to find a common positive-definite symmetric matrix in each maximal overlapped-rules group, can reduce the conservatism and difficulty of the former stability analysis approaches. Using the method of parallel distributed compensation, a systematic design approach of T–S fuzzy control systems is presented. The simulation results of three examples show that these methods are effective.