Robust finite-time H 1 control for a class of uncertain switched neutral systems Zhengrong Xiang a,⇑ , Ya-Nan Sun a , Magdi S. Mahmoud b a School of Automation, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China b Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 5067, Dhahran 31261, Saudi Arabia article info Article history: Received 8 May 2011 Received in revised form 17 August 2011 Accepted 13 September 2011 Available online 24 September 2011 Keywords: Switched neutral systems Finite-time boundedness Finite-time H 1 performance Finite-time H 1 control abstract This paper investigates the robust finite-time H 1 control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance. The uncertainties under consideration are norm bounded. By using the average dwell time approach, a suf- ficient condition for finite-time boundedness of switched neutral systems is derived. Then, finite-time H 1 performance analysis for switched neutral systems is developed, and a robust finite-time H 1 state feedback controller is proposed to guarantee that the closed- loop system is finite-time bounded with H 1 disturbance attenuation level c. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Switched system is an important class of hybrid system, which consists of a family of subsystems and a switching rule specifying which subsystem will be activated along the system trajectory at a time instant. In the last decades, switched sys- tems have received considerable attentions for their significant application in various fields, and a great number of excellent works have been developed (see [1,2], and the references cited therein). It is well known that the time-delays as inherent features of many dynamic systems, exist widely in practical engineering systems and may cause instability or undesirable system performance. Over the past decades, a great deal of progress has been made on the research of time-delay system (see [3,4]). Neutral system is a special class of time-delay system, which depends not only on the delays of state but also on the delays of state derivative. The primary motivation for studying such neutral system comes partly from the fact that neutral system has numerous applications in the control of engineering and social systems, such as networks, heat exchanges, and processes including steam [5]. In addition, there exist a large number of time-delay systems which can be transformed into neutral systems. Over the years, many research efforts have been devoted to the study of switched neutral systems (see [6–14]). To name a few, the problem of stability and control synthesis was developed for a class of switched neutral systems in [9,10], the prob- lem of robust non-fragile H 1 control and reliable H 1 control for switched neutral systems were investigated in [12,13], respectively, and the issue of robust sliding mode control for uncertain switched neutral systems was discussed in [14]. However, most of the existing literature has focused on Lyapunov asymptotic stability for switched neutral systems, the behavior of which is over an infinite time interval. Lyapunov asymptotic stability depicts steady state performance of a dy- namic system, and it could not reflect transient state performance. There exists a system that is asymptotically stable but could be unusable in practical engineering for its bad transient characteristics. For the systems which work in a short time 1007-5704/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2011.09.022 ⇑ Corresponding author. E-mail addresses: xiangzr@mail.njust.edu.cn (Z. Xiang), msmahmoud@kfupm.edu.sa (M.S. Mahmoud). Commun Nonlinear Sci Numer Simulat 17 (2012) 1766–1778 Contents lists available at SciVerse ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns