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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 832891, 11 pages
http://dx.doi.org/10.1155/2014/832891
Research Article

Robust Guaranteed Cost Observer Design for Singular Markovian Jump Time-Delay Systems with Generally Incomplete Transition Probability

1School of Mathematical Sciences, Guangxi Teachers Education University, Guangxi 530001, China
2Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
3College of Information Science and Engineering, Ocean University of China, Qingdao 266071, China

Received 29 November 2013; Revised 6 February 2014; Accepted 10 February 2014; Published 24 March 2014

Academic Editor: Shen Yin

Copyright © 2014 Yanbo Li 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 is devoted to the investigation of the design of robust guaranteed cost observer for a class of linear singular Markovian jump time-delay systems with generally incomplete transition probability. In this singular model, each transition rate can be completely unknown or only its estimate value is known. Based on stability theory of stochastic differential equations and linear matrix inequality (LMI) technique, we design an observer to ensure that, for all uncertainties, the resulting augmented system is regular, impulse free, and robust stochastically stable with the proposed guaranteed cost performance. Finally, a convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters for linear singular Markovian jump time-delay systems with generally incomplete transition probability.