Improved robust stability and feedback stabilization criteria for time-delay systems

Abstract

This paper develops novel robust stability and feedback stabilization criteria with guaranteed performance for a class of linear continuous time-delay systems with polytopic uncertainties. The time-varying delay function is unknown and differentiable within bounded interval and the input delay is constant. The criteria is derived based on the constructive use of a new Lyapunov–Krasovskii functional together with the integral inequality. The developed stability condition is expressed in terms of linear matrix inequality that manipulates fewer decision variables and requires reduced computational load. Through a comparison with other existing stability methods, it is established that the developed method retains some useful terms that are frequently dropped out and does not employ any free-weighting matrices to avoid redundancy. A state-feedback stabilizing controller is designed to ensure that the closed loop is robustly stable with guaranteed performance. Representative examples are simulated to illustrate the developed results.