H_∞ model reduction for discrete-time Markov jump linear systems with partially known transition probabilities

Abstract

In this article, the H _∞ model reduction problem for a class of discrete-time Markov jump linear systems (MJLS) with partially known transition probabilities is investigated. The proposed systems are more general, relaxing the traditional assumption in Markov jump systems that all the transition probabilities must be completely known. A reduced-order model is constructed and the LMI-based sufficient conditions of its existence are derived such that the corresponding model error system is internally stochastically stable and has a guaranteed H _∞ performance index. A numerical example is given to illustrate the effectiveness and potential of the developed theoretical results.

Keywords:

• Markov jump linear systems
• H _∞ model reduction
• partially known transition probabilities
• linear matrix inequality (LMI)