Delay-Dependent Robust Stabilization for Time-varying Delay Uncertain Systems with Actuator Saturation

In this paper, the problems of stabilization criteria for a class of linear time-varying delay uncertain systems with saturating actuator are derived. Based on the Lyapunov-Krasovskii functional combining with LMI techniques and Leibniz-Newton formula, delay-dependent stabilization criteria are derived for the existence of a state feedback controller, which ensures asymptotic stability of the closed systems for all admissible uncertainties. Furthermore, we try to transform the LMI feasible problem into the equivalent generalized eigenvalue problem (GEVP). Such that the global solution, namely the maximum upper bound on the admissible delay, can be determine by using the LMI toolbox in Matlab. Finally, two numerical examples are given to demonstrate the feasibility and solve the generalized eigenvalue minimization problem (GEVP) of our proposed approach.