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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 872158, 11 pages
http://dx.doi.org/10.1155/2014/872158
Research Article

Finite-Time -Gain Control for Positive Switched Systems with Time-Varying Delay 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 21 November 2013; Accepted 14 December 2013; Published 23 January 2014

Academic Editor: Hui Zhang

Copyright © 2014 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.

Abstract

This paper is concerned with the problem of finite-time -gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee the -gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both continuous and discrete systems into the delta operator framework. Then, based on the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with an -gain performance. Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the proposed method.