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

In this paper, the stochastic stabilizability and H∞ disturbance attenuation are studied for discrete-time linear time-delay systems that possess randomly jumping parameters using the linear matrix inequality approach. The transition of the jumping parameters is governed by a finite-state Markov process. A sufficient condition is first established on the stochastic stability using the stochastic Lyapunov functional approach. Then sufficient conditions on the existence of a stochastic stabilizing and γ-suboptimal H∞ state feedback controller are presented. It is shown that the stochastic stabilizing H∞ state feedback controller can be constructed through numerical solution of a set of coupled linear matrix inequalities. The state delay systems are first treated and extension to a class of general delay systems are then considered.