Stabilization of Discrete-Time Hidden Semi-Markov Jump Singularly Perturbed Systems With Partially Known Emission Probabilities

This article considers the stabilization problem of discrete-time semi-Markov jump singularly perturbed systems, in which the system operation mode is hidden but can be estimated by a detector with some emission probabilities. To model this circumstance, the hidden semi-Markov model (HSMM) with partially known emission probabilities is introduced, where the hidden state represents the real system operation mode while the emitted value represents the estimated value of the system operation mode and is available for the stabilizing controller. Based on the introduced HSMM, the stabilizing controller which only relies on the estimated value is designed to guarantee the
$\delta$
-error mean square stability of the closed-loop system. A numerical example is used to verify the usefulness of the obtained results.