Model Reduction of Markovian Jump Systems With Uncertain Probabilities

Abstract

This paper studies the problem of model reduction for nonhomogeneous Markovian jump systems. The transition probability matrix of the nonhomogeneous Markovian chain has the characteristic of a polytopic structure. An asynchronous reduced-order model is considered, and the asynchronization is modeled by a hidden Markov model with a partially unknown conditional probability matrix. Under this framework, a new sufficient condition is proposed to ensure that the augmented system is stochastically mean-square stable with a specified level of $H_\infty$ performance. Finally, a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained.