I. Introduction

During the past decade, fuzzy control based on Takagi–Sugeno (T–S) fuzzy systems has been used widely to nonlinear control systems, and systematic design for T–S fuzzy systems has been studied [1]–[9]. Based on the parallel distributed compensation, Tanaka et al. [10], [11] presented the primary stabilization criteria for T–S fuzzy systems. After that, many studies were devoted to get relaxed stabilization criteria for T–S fuzzy systems. Based on common quadratic Lyapunov functions, relaxed criteria for T–S fuzzy systems have been proposed by different kinds of relaxing techniques [12]–[18]. Moreover, other studies utilized piecewise Lyapunov functions [19]–[23] or nonquadratic Lyapunov functions [24]–[29] to analyze T–S fuzzy control systems. Since piecewise quadratic Lyapunov functions and nonquadratic Lyapunov functions are much richer classes of Lyapunov function candidates than common quadratic Lyapunov functions, the conservatism of the common quadratic Lyapunov function analysis can be reduced by applying piecewise Lyapunov functions [30] or nonquadratic Lyapunov functions [31]. in [30], minimum-type and maximum-type piecewise Lyapunov functions were proposed to get relaxed stability criteria for linear time-varying systems. To the authors’ knowledge, these two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions have not been employed for the controller synthesis of T–S fuzzy systems.