A Robust Fuzzy Control Approach to Stabilization of Nonlinear Time-delay Systems with Saturating Inputs

Abstract

This paper deals with the stabilization of uncertain nonlinear time-delay systems subject to input saturation. A nonlinear time-delay system is first represented by Takagi-Sugeno (T-S) fuzzy model, a set of fuzzy implications which are used to characterize local dynamics with actuator saturation. Based on a delay independent stability analysis, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is determined. The fuzzy control law is then developed to maximize the estimation of this domain. The derived conditions are formulated in terms of linear matrix inequalities (LMIs) so that the synthesis of fuzzy controller and the estimation of stability domain can be carried out efficiently. Moreover, a robust stabilization for systems with parameter uncertainties, which are time-varying and norm-bounded, is discussed. Numerical examples of truck-trailer control are provided to demonstrate the effectiveness of the design.