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Mathematical Problems in Engineering
Volume 2013, Article ID 364726, 9 pages
http://dx.doi.org/10.1155/2013/364726
Research Article

Sliding Sector-Based Variable Structure Control of Continuous-Time Markov Jump Linear Systems Subject to Unknown Transition Rates

1The School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044, China
2The School of Automation, Southeast University, Nanjing, Jiangsu 210096, China

Received 8 August 2013; Accepted 5 October 2013

Academic Editor: Tao Li

Copyright © 2013 Yan-Mei Xue 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

Based on sliding sector technique, the variable structure control for a class of uncertain continuous-time Markovian jump linear systems (MJLS) is investigated. The elements in the transition rate matrix include completely known, boundary known, and completely unknown ones. First, the related notions about sliding sector for continuous-time Markov jump linear systems are given; then based on linear matrix inequalities (LMIs) technique, sufficient conditions for the design of the sliding sector are provided. Second, a variable structure control law is presented to guarantee the mean-square quadratic stability of the closed-loop system in spite of the effects of the existing uncertainties and unknown/uncertain transition rates. Finally, an example is given to verify the validity of the theoretical results.