Passivity-Based Control for Hidden Markov Jump Systems With Singular Perturbations and Partially Unknown Probabilities

Abstract

In this article, the passivity-based control problem is addressed for hidden Markov jump systems with singular perturbations and partially unknown probabilities. The hidden Markov model (HMM) with partially unknown probabilities is introduced, where the partially unknown probabilities may exist in either the transition probability matrix of Markov chain, the observation probability matrix of observed signal, or in both of them. Thus, the underlying HMM is more general than the one in some existing works. By using this HMM, some passivity analysis criteria are established for Markov jump singularly perturbed systems with partial unknown probabilities. Based on these criteria, a unified method is presented for the design of controllers to ensure the passivity of the system. A numerical example and an armature controlled dc motor model are given to illustrate the efficiency of the proposed method.