Mixed control of uncertain jumping time-delay systems

In this paper, we investigate a class of linear continuous-time systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state with time-varying and bounded delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Employing norm-bounded parametric uncertainties and utilizing the second-method of Lyapunov, we examine the problem of designing a mixed H 2 / H ∞ controller which minimizes a quadratic H 2 performance measure while satisfying a prescribed H ∞ -norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the mixed H 2 / H ∞ controller and the associated performance upper bound could be cast in the form of linear matrix inequalities.