Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals

This paper considers the problem of robust stability and robust stabilization for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent quadratic stability results, demonstrate that it allows the use of parameter-dependent Lyapunov functionals, and develop control design methods based on linear matrix inequalities (LMIs) for solving the robust control problem. Next, the problem of determining the maximum time-delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, illustrative examples are given to demonstrate the advantage of these new representations.