Fuzzy Lyapunov decentralized control of Takagi-Sugeno interconnected descriptors

Abstract

This paper deals with decentralized stabilization of nonlinear systems composed of interconnected Takagi-Sugeno fuzzy descriptors. To ensure the stability of the overall closed-loop system, a set of decentralized Parallel Distributed Compensations (PDC) controllers is employed. The stability conditions are then derived into Linear Matrix Inequalities (LMI) using a fuzzy Lyapunov function for less conservatism. Nevertheless, it contains decision parameters that are not available in practice. So the LMIs are casted into relaxed quadratic conditions using simple assumptions. Finally, a numerical example is proposed to illustrate the effectiveness of the suggested decentralized approach.