Refined Stability Conditions for Linear Uncertain Systems With Multiple Time-Varying Delays

Abstract

This paper mainly proposes distinct criteria for the stability analysis and stabilization of linear uncertain systems with time-varying delays. Based on the Lyapunov theorem, a sufficient condition of the unforced systems with single time-varying delay is first derived. By involving a memoryless state feedback controller, the condition will be extended to treat with the resulting closed-loop system. These explicit criteria can be reformulated in LMIs forms, so we will readily verify the stability or design a stabilizing controller by the current LMI solver. Furthermore, the considered systems with multiple time-varying delays are similarly addressed. Numerical examples are given to demonstrate that the proposed approach is effective and valid.