New stability method applied to the stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a new stability method previously developed and presented by the authors. The new stability method is here extended to fuzzy systems. In essence, the authors consider the stabilization of a fuzzy control system with parallel distributed compensation. This problem has been considered in detail previously by different authors using fuzzy Lyapunov function theory. However, in this paper the authors show that their new stability method presents a viable alternative to Lyapunov's method for such control systems. This statement is confirmed by a demonstration that the new stability method always provides necessary and sufficient conditions, the satisfaction of which guarantees that the system in question will be asymptotically stable.