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Mathematical Problems in Engineering
Volume 2015, Article ID 852303, 10 pages
Research Article

Robust Control for Switched Nonlinear System with Multiple Delays

1College of Mathematics, Jilin University, Changchun 130012, China
2Shenyang University, Shenyang 110044, China

Received 20 January 2015; Revised 13 April 2015; Accepted 16 April 2015

Academic Editor: Carlo Cosentino

Copyright © 2015 Juan Liu and Qingdao Huang. 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 focuses on the problem of robust control for a class of switched nonlinear systems with multiple time delays which are allowed to appear not only in state but also in input. We will design a controller and a switching law under which the system is “robust stable” and has performance -gain . Besides, multiple Lyapunov-Razumikhin functions which are relatively less conservative are introduced to investigate the stability of the candidate switched system. In detail, firstly, for uncertain nonlinear switched system with time-varying delays, sufficient condition is given by inequalities which are equivalent to LMIs, so it is easy to be solved; then, as a special case, nonlinear switched system with constant time delay is also considered. Finally, by providing numerical examples, the feasibility of the proposed approach is demonstrated.