Guaranteed Cost Control for Singular Markovian Jump Systems with Time Delay

This paper is concerned with delay-dependent guaranteed cost control (GCC) problem for uncertain singular time-delay systems with Markovian jumping parameters. In terms of linear matrix inequality (LMI) approach, the sufficient conditions are proposed for singular Markovian jump systems with time-delay to be stochastically admissible. Based on this, the sufficient conditions are obtained for the existence of guaranteed cost controller, which guarantees the uncertain singular Markovian jump systems with time-delay to be regular, impulse free and stochastically stable and the quadratic cost function smaller than an upper bound. The explicit expression of the guaranteed cost controller is also characterized by solving a set of LMIs. Numerical example is given to show the effectiveness of the proposed method.