Robust exponential stabilization for uncertain systems with state and control delay

This paper is concerned with the issue of robust stabilization for uncertain time-delay systems in which delay terms appear as both states and controls. The uncertain time-delay systems under consideration are described by state differential equations with time-invariant unknown but bounded delays. Based on the Lyapunov–Krasovskii functional method, exponential stabilization criteria are also derived. Our results, which are given in terms of quadratic forms of state, depend on the size of the delay and are more informative and accurate. This is because the proposed methods have not included any supplementary conditions on the system's matrix. Thus, the proposed criteria in general are less conservative than existing ones and successfully avoid all existing problems. The results are illustrated with numerical examples. We believe that the proposed schemes are applicable to robust control design.