Robust output feedback H∞ control of uncertain Markovian jump systems with mode-dependent time-delays

This paper describes the synthesis of robust output feedback H1 control for a class of uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system modes of operation. Under the assumption of known bounds of system uncertainties and the control system gain variations, we present sufficient conditions on the existence of robust stochastic stability and -disturbance H1 attenuation. Through the changes of variables and Schur complements, these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities, with which, robust control can be easily constructed. As an added advantage, the control design depends only on pmj, t, the measured parameter of Markovian jumping at time t, which might be corrupted by measurement noises. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.