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Mathematical Problems in Engineering
Volume 2013, Article ID 495194, 8 pages
Research Article

Control of Singular Markovian Jump Systems with Bounded Transition Probabilities

1Department of Preparatory Course, Shenyang Institute of Engineering, Shenyang 110036, China
2School of Information and Control Engineering, Liaoning Shihua University, Liaoning, Fushun 113001, China

Received 10 October 2013; Accepted 20 November 2013

Academic Editor: Hao Shen

Copyright © 2013 Hongsheng Lin 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.


This paper discusses control problems of continuous-time and discrete-time singular Markovian jump systems (SMJSs) with bounded transition probabilities. Improved sufficient conditions for continuous-time SMJSs to be regular, impulse free, and stochastically stable with -disturbance attenuation are established via less conservative inequality to estimate the transition jump rates, so are the discrete-time SMJSs. With the obtained conditions, the design of a state feedback controller which ensures the resulting closed-loop system to be stochastically admissible and with performance is given in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and the benefits of the proposed approaches.