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Abstract and Applied Analysis
Volume 2014, Article ID 871591, 11 pages
Research Article

A New Finite-Time Bounded Control of Stochastic Itô Systems with ( )-Dependent Noise: Different Quadratic Function Approach

1School of Electrical Engineering and Automation, Qilu University of Technology, Jinan 250353, China
2State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China

Received 24 November 2013; Accepted 11 January 2014; Published 24 March 2014

Academic Editor: Hui Zhang

Copyright © 2014 Zhiguo Yan and Zhongwei Lin. 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 addresses the finite-time bounded control problem of linear stochastic systems with state, control input, and external disturbance-dependent noise (( )-dependent noise for short). The notion of finite-time boundedness of linear stochastic systems is first introduced. Then a different quadratic function approach is proposed to give a sufficient condition for finite-time boundedness of such a class of systems, and its superiority to common quadratic approach is shown. Moreover, the finite-time bounded controller design problem is studied and two sufficient conditions for the existence of state and output feedback controllers are presented in terms of nonlinear matrix inequalities. An algorithm is given for solving the obtained nonlinear matrix inequalities. Finally, an example is employed to illustrate the effectiveness of our obtained results.