Robust H∞ control for uncertain descriptor time-delay systems with Markov jumping parameters

This paper deals with the robust stabilizability and H-infinity disturbance attenuation for a class of uncertain descriptor time-delay systems with jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. A sufficient condition on robust stabilizability is established based on the stability theory for stochastic differential equations. With the help of a set of coupled linear matrix inequalities, robust 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.