Stochastic stabilizability and H-infinity control for discrete-time jump linear systems with time delay

In this paper, the stochastic stabilizability and H-infinity disturbance at tenuation are studied for discrete-time linear time-delay systems that poss ess randomly jumping parameters using the linear matrix inequality approach . The transition of the jumping parameters is governed by a finite-state Ma rkov process. A sufficient condition is first established on the stochastic stability using the stochastic Lyapunov functional approach. Then sufficie nt conditions on the:existence of a stochastic stabilizing and gamma-subopt imal H-infinity state feedback controller are presented. It is shown that t he stochastic stabilizing H-infinity state feedback controller can be const ructed through numerical solution of a set of coupled linear matrix inequal ities. The state delay systems are first treated and extension to a class o f general delay systems are then considered. (C) 2000 The Franklin Institut e. Published by Elsevier Science Ltd. All rights reserved.