Further Results on Robust Exponential Stabilization for Time-varying Delay Saturating Actuator Systems with Delay-dependence

Abstract

The problem of delay-dependent exponential robust stabilization for a class of uncertain saturating actuator systems with time-varying delay is investigated. Novel exponential stability and stabilization criteria for the system are derived using the Lyapunov-Krasovskii functional combined with Leibniz-Newton formula. The issue of exponential stabilization for time-varying delay systems with saturating actuator using generalized eigenvalue problem (GEVP) approach remains open, which motivates this paper. The designed controller is dependent on the time-delay and its rate of change. All the conditions are presented in terms of linear matrix inequalities (LMIs), which can solved efficiently by using the convex optimization algorithms. A state feedback control law is also given such that the resultant closed-loop system is stable for admissible uncertainties. Two numerical examples are given to demonstrate the efficiency of the obtained results.