Comments on “Generalization of stability criterion for Takagi–Sugeno continuous fuzzy model”

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

“…Buckley [3] had proven that T-S fuzzy systems are universal approximators. During the past several years, many scholars have been studying the stability analysis and systematic design of T-S fuzzy systems [1,[4][5][6][7][8][9][10][11][13][14][15][16][17][18]. Tanaka and Sugeno [14] ÿrstly proposed a stability analysis and design method for T-S fuzzy systems.…”

“…Cao et al [6] proposed an approach for stability analysis and synthesis of nonlinear time-delay systems via linear T-S fuzzy models. Matia et al [9,10] presented several stability conditions of a generalized class of continuous fuzzy systems, in which the o set terms are not equal to zero. Feng et al [7] discussed fuzzy model reference adaptive control for a class of nonlinear systems.…”

“…They proposed a stability condition for fuzzy systems in which di erent quadratic Lyapunov functions in di erent operating regions were searched to constitute a continuous Lyapunov function in the global state space. Zhang et al [18] employed a maximum defuzziÿer to avoid the di culty of ÿnding a common positivedeÿnite matrix P. Among these approaches, [1,6,9,10,[13][14][15][16][17] disregarded the structural information encoded in the rule's promises. However, in practical application, the fuzzy membership functions of input variables of most fuzzy control systems have bounded support and a subsystem is only valid in a limited region of the state space.…”