On Robust Switched Controller Design to Minimize the Guaranteed Cost of Polynomial Fuzzy Systems

Abstract

This paper presents a robust switched controller design to minimize an upper bound of a quadratic index (guaranteed cost) based on the output and the control input of uncertain nonlinear systems described by polynomial fuzzy models (PFM). The proposed switched controller is based on the minimization of the derivative of the Lyapunov function and does not require the knowledge of the membership functions to compose the control signal, which may be uncertain or whose obtainment may be difficult. The class of nonlinear systems considered in this paper can be exactly described by PFM, and it is possible to obtain a global model representation without the specification of an operation region. A numerical example illustrates the effectiveness of the proposed switched controller and presents a comparative study with the results obtained using a controller composed only of a single gain.