Robust H∞ control of uncertain Markovian jump systems with time-delay

This paper is concerned with the robust stochastic stabilizability and robust H_∞ disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. Sufficient conditions on the existence of a robust stochastic stabilizing and γ-suboptimal H_∞ state-feedback controller are presented using the Lyapunov functional approach. It is shown that a robust stochastically stabilizing H_∞ state-feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities