On robust stability for uncertain time-delay systems: A polyhedral Lyapunov-Krasovskii approach

In this paper, the problem of robust stability for a class of time-delay systems is investigated. The uncertainties possessed in the systems are assumed to be time invariant and belong to a convex bounded polytopic domain. For comparison, both single polyhedral and double polyhedral Lyapunov functionals are defined according to the form of a Lyapunov-Krasovskii functional. Robust stability results are obtained by using the double polyhedral Lyapunov functional approach. Also, for a known convex uncertainty subdomain, two equivalent conditions are presented. All established stability conditions are expressed in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and usefulness of the main theoretic results.