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Mathematical Problems in Engineering
Volume 2015, Article ID 950685, 9 pages
http://dx.doi.org/10.1155/2015/950685
Research Article

Robust Finite-Time Control for Linear Time-Varying Descriptor Systems with Jumps

School of Science, Shenyang University of Technology, Shenyang 110870, China

Received 30 December 2014; Revised 9 March 2015; Accepted 10 March 2015

Academic Editor: Valter J. S. Leite

Copyright © 2015 Xiaoming Su and Adiya Bao. 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

The finite-time control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-time for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfies gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.