On the problems of robust stability and stabilization for uncertain discrete-time singular Markovian jump system

The problems of robust stability and stabilization for uncertain discrete-time singular Markovian jump system is addressed in this paper. Firstly, a necessary and sufficient condition for a discrete-time singular Markovian jump system(MJL) to be stochastically admissible is proposed in terms of a strict linear matrix inequality(LMI). On the basis of this, the concepts of generalized quadratic stochastical stability and generalized quadratic stochastical stabilization for uncertain discrete-time MJL systems are introduced. Then Necessary and sufficient conditions for generalized quadratic stochastical stability and generalized quadratic stochastical stabilization are derived in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of stochastically robust stability and stochastically robust stabilization are solved. An explicit expression of a desired state feedback controller is also given.