A dual design problem via multiple Lyapunov functions

摘要

This paper presents a dual design problem via multiple Lyapunov functions. Based on a multiple Lyapunov approach, we introduce two important concepts. One is a dual design concept that minimizes/maximizes upper bounds of the time derivative of premise membership functions in a Takagi-Sugeno fuzzy system. The other is a stability margin concept for switching speed among if-then rules. It is related to avoiding conservatism of stability analysis and guaranteeing system response performance. A design example illustrates the utility of the dual design via the multiple Lyapunov function approach.