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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 263045, 10 pages
http://dx.doi.org/10.1155/2014/263045
Research Article

Finite-Time Stability and Stabilization of Itô-Type Stochastic Singular Systems

1School of Electrical Engineering and Automation, Qilu University of Technology, Jinan 250353, China
2College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China

Received 14 October 2013; Accepted 19 November 2013; Published 14 January 2014

Academic Editor: Hui Zhang

Copyright © 2014 Zhiguo Yan and Weihai Zhang. 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 concerned with the finite-time stability and stabilization problems for linear Itô stochastic singular systems. The condition of existence and uniqueness of solution to such class of systems are first given. Then the concept of finite-time stochastic stability is introduced, and a sufficient condition under which an Itô stochastic singular system is finite-time stochastic stable is derived. Moreover, the finite-time stabilization is investigated, and a sufficient condition for the existence of state feedback controller is presented in terms of matrix inequalities. In the sequel, an algorithm is given for solving the matrix inequalities arising from finite-time stochastic stability (stabilization). Finally, two examples are employed to illustrate our results.