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

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.