Stochastic stabilization and H∞ control for linear jump systems with distributed delays

This paper deals with the stochastic stabilizability and H-infinity disturbance attenuation for a class of linear jump systems with discrete and distributed delays. The transition of the jumping parameters in the system is governed by a finite-state Markov process. A sufficient condition on stochastic stabilizability is estabilished based on the stability theory for stochastic differential equations. With the help of a set of coupled linear matrix inequalities, stochastic H-infinity controllers are designed to stochastically stabilize the given systems with a prescribed disturbance attenuation level represented by an H-infinity norm bound constraint. A numerical example demonstrates the effect of the proposed design approach.