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Mathematical Problems in Engineering
Volume 2013, Article ID 537174, 11 pages
http://dx.doi.org/10.1155/2013/537174
Research Article

Model Reduction for Discrete-Time Markovian Jump Systems with Deficient Mode Information

1Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 4 April 2013; Accepted 3 June 2013

Academic Editor: Xiaojie Su

Copyright © 2013 Yanling Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the problem of model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a new performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex linearisation approach and iterative approach, for the model reduction synthesis are proposed. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design methods.