Robust control for uncertain systems with time-delay and jump parameters *

Abstract

This paper is concerned with the robust stochastic stabilization and H ∞ disturbance attenuation for uncertain discrete-time Markovian jump linear time-delay systems subject to norm-bounded parameter uncertainties. The transition of the jumping parameters is governed by a finite-state Markov process. First a sufficient condition on stochastic stability is proposed using the stochastic Lyapunov functional approach. Then sufficient conditions on robust stochastic stabilizing and γ-suboptimal H ∞ memoryless state feedback controllers are presented. It is shown that a stochastic stabilizing H ∞ state feedback controller can be constructed through numerical solution of a set of coupled linear matrix inequalities.