Stabilization for fast sampling discrete-time singularly perturbed singular Markovian systems

This paper considers the problems of stabilization and $H_{\infty }$ control for fast sampling discrete-time singularly perturbed singular Markovian systems (SPSMSs). The system equivalent approach is initially introduced to transform the discrete fast sampling SPSMS model into the augmented SPSMS for the convenience of designing system controller. Secondly, sufficient condition on stochastically mean square admissibility is established for the fast sampling SPSMS. By separating matrix variables and singularly perturbed parameter, a state feedback controller is also provided to ensure stochastically mean square admissibility of the fast sampling augmented SPSMS. Then, the results are extended to $H_{\infty }$ performance analysis and controller design in the presence of the external disturbances. The derived criteria can be converted to the feasible problems based on convex optimization, and the upper bound of singular perturbation parameter is also calculated. Besides, a discretized electrical circuit system is provided to verify the effectiveness and the superiority of the proposed approach.