Relaxed LMI-based stability analysis of fuzzy model-based control systems using approximated polynomial membership functions

Abstract

Relaxed LMI-based stability conditions for fuzzy model-based (FMB) control systems are proposed. Considering LMI-based shape-dependent stability conditions, containing relations between state variables and membership functions, some more relaxed stability conditions for FMB control systems with `Parallel Distributed Compensation'(PDC) design technique are derived. In the aforementioned approach, product terms of fuzzy model and fuzzy controller membership functions are approximated by polynomials in the partitioned operating domain of membership functions so that corresponding to each sub-region a proper polynomial for each product term is derived. However, conservativeness, resulting from considering the whole operating region for approximated polynomials still remains. In this paper, to release this conservativeness, the concept of S-procedure is exploited. One Simulation example is presented to illustrate the validity of the proposed approach.