Improved results on H∞ model reduction for Markovian jump systems with partly known transition probabilities

This paper is concerned with the model reduction problem for Markovian jump systems with partly known transition probabilities. By making use of an existing result on the convex properties of the transition probabilities, an improved condition is first derived for the H∞ performance analysis of the error system. Two different approaches, one in terms of linear matrix inequalities (LMIs) and another in the form of an iterative algorithm subject to LMI constraints, are then proposed to find a reduced-order model such that the H∞ performance of the error system is bounded by a specified level. The first approach is obtained using Finsler's Lemma, and involves fewer decision variables than the existing method. It is shown that the proposed methods cover some existing results as special cases. Finally, the advantages of our results are clearly illustrated by a numerical example.