An LMI approach to fuzzy controller designs based on relaxed stability conditions

Abstract

New stability conditions satisfying decay rate are derived for both continuous and discrete fuzzy control systems. LMI (linear matrix inequality) based design procedures that consider decay rate and constraints on control input and output are constructed using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate and constraints on control input and output. Design examples demonstrate the effectiveness of the LMI-based designs proposed in this paper.