Non-fragile H∞ control for a class of discrete Markovian Jump linear systems with time delay

This paper is concerned with the problem of linear state feedback in the presence of controller gain variations for a class of discrete-time Markovian jump linear systems (MJLs) with time delay. The controller gain to be designed is assumed to have additive norm-bounded variations. A sufficient conditions on the existence of a stochastic stabilizing and γ-disturbance attenuation H_∞ non-fragile state feedback controller are provided. It is shown that the controller can be constructed through numerical solution of a set of coupled linear matrix inequalities. The state delay systems are first treated and extention to a class of general delay systems are then considered.