Robust Stability Analysis and Feedback Control for Uncertain Systems with Time-Delay and External Disturbance

Abstract

This paper addresses the delay-dependent Takagi-Sugeno (T-S) fuzzy state feedback control and exponential admissibility analysis for a class of T-S fuzzy singular uncertain systems. Firstly, the T-S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input and unmatched disturbance. Secondly, the delay-dependent T-S fuzzy state feedback controller is designed by employing the T-S fuzzy model. Thirdly, the free-weighting matrices and delay-dependent Lyapunov-Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T-S fuzzy state feedback controller is designed for the T-S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.