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Mathematical Problems in Engineering
Volume 2013, Article ID 515362, 10 pages
Research Article

Stability and -Gain Control of Positive Switched Systems with Time-Varying Delays via Delta Operator Approach

1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 15 September 2013; Accepted 6 November 2013

Academic Editor: Xiaojie Su

Copyright © 2013 Shuo 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.


This paper investigates the problems of stability and -gain controller design for positive switched systems with time-varying delays via delta operator approach. The purpose is to design a switching signal and a state feedback controller such that the resulting closed-loop system is exponentially stable with -gain performance. Based on the average dwell time approach, a sufficient condition for the existence of an -gain controller for the considered system is established by constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant methods in the literature of both continuous- and discrete-time systems into the delta operator framework. Finally, a numerical example is presented to explicitly demonstrate the effectiveness and feasibility of the proposed method.