INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust. Nonlinear Control (2012) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/rnc.2777 Stability of a class of switched positive linear time-delay systems Xudong Zhao 1, * ,† , Lixian Zhang 2 and Peng Shi 3,4 1 College of Information and Control Engineering, China University of Petroleum, Qingdao 266555, China 2 Space Control and Inertial Technology ResearchCenter,Harbin Institute of Technology, Harbin 150001, China 3 Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd CF37 1DL, UK 4 School of Engineering and Science, Victoria University, Melbourne, 8001 Vic, Australia SUMMARY This paper addresses the problem of stability for a class of switched positive linear time-delay sys- tems. As first attempt, the Lyapunov–Krasovskii functional is extended to the multiple co-positive type Lyapunov–Krasovskii functional for the stability analysis of the switched positive linear systems with constant time delay. A sufficient stability criterion is proposed for the underlying system under average dwell time switching. Subsequently, the stability result for system under arbitrary switching is presented by reducing multiple co-positive type Lyapunov–Krasovskii functional to the common co-positive type Lyapunov–Krasovskii functional. A numerical example is given to show the potential of the proposed techniques. Copyright © 2012 John Wiley & Sons, Ltd. Received 29 March 2011; Revised 15 October 2011; Accepted 12 November 2011 KEY WORDS: multiple co-positive Lyapunov–Krasovskii functional; stability; switched positive linear systems; time delay 1. INTRODUCTION In the past decade, positive systems have drawn considerable interest because of their numerous applications in areas such as economics, biology, communications, and so on [1,7,11]. Very recently, switched positive linear systems (SPLS), which consist of a family of positive linear systems and a switching signal governing the switching among them, have also been paid much attention in con- trol communities. Typical applications of these systems can be also found in many fields, congestion control applications [3, 22], formation flying [10], and networks employing TCP [18], to mention a few. So far, useful results for SPLS have been obtained in the literature, particularly with respect to the stability analysis. It is noted that the non-negativity of each state vector element for all times of positive systems will bring about some difficulties, which cannot be solved by using well-developed methods for general linear systems [2, 11, 13]. In practice, time-delay phenomena in dynamic systems widely exist. Although many results have been reported for time-delay systems [12, 17, 26–28], only recently has the positive linear systems with time delay become a topic of major interest. To list a few, necessary and sufficient stability criteria for positive systems with constant delay are obtained in [6] by means of linear co-positive Lyapunov functional, which is a powerful tool for tackling positive systems [16,18], sufficient sta- bility conditions for delayed positive systems with uncertainties are given in [4], and the constrained control and observer design problems are considered in [9,23]. However, it is worth mentioning that up to date, there are little effort put on SPLS in the presence of time delay, which is theoretically challenging and of fundamental importance to numerous applications [13]. *Correspondence to: Xudong Zhao, College of Information and Control Engineering, China University of Petroleum, Qingdao 266555, China. † E-mail: xdzhaohit@gmail.com Copyright © 2012 John Wiley & Sons, Ltd.