Model reduction for a class of nonstationary Markov jump linear systems

This paper concerns the problem of model reduction for a class of Markov jump linear system (MJLS) with nonstationary transition probabilities (TPs) in discrete-time domain. The nonstationary character of TPs is considered as finite piecewise stationary and the variations in the finite set are considered as two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix. Invoking the idea in the recent studies of partially unknown TPs for the traditional MJLS with stationary TPs, a generalized framework covering the two kinds of variation is proposed. The model reduction results for the underlying systems are obtained in H∞ sense. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.