Stability analysis for a class of switched neutral systems via multiple generalized Lyapunov functionals scheme Tai-Fang Li 1,2 , Mingshun Wang 1,2 , Georgi M. Dimirovski 3,4 and Jun Zhao 1,2 1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, P.R. China 2. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, P.R. China E-mail: xiaofang0412@163.com , zhaojun@mail.neu.edu.cn 3. The School of Engineering, Dogus University, 34722 Istanbul, Republic of Turkey 4. The School of FEIT, SS Cyril and Methodius University, 1000 Skopje, Republic of Macedonia E-mail: gdimirovski@dogus.edu.tr Abstract: This paper discusses the stability analysis for a class of switched neutral systems with none of the individual subsystems asymptotically stable. By employing a multiple generalized Lyapunov functionals method and a free weighting matrix technique, a delay-dependent stability criterion under a hysteresis switching law is developed in terms of linear matrix inequalities (LMIs). Finally, an example illustrates the proposed method. Key Words: Hysteresis switching, switched neutral systems, time-varying delay, multiple generalized Lyapunov functionals 1 Introduction Time-delay is the inherent feature of many physical process and frequently a big source of poor system performance, or instability [1-3]. Neutral systems, which contain delays both in their states and in the derivatives of their states, have been found in many engineering applications. In the last two decades, neutral systems have attracted much attention (see [4-7] and the references therein). Other the other hand, switched systems as an important class of hybrid systems that consist of several subsystems and a logical rule to determine which subsystem is active at certain time interval. The widespread applications of switched systems are motivated by increasing performance requirements in control, such as chemical processing, communication networks, traffic control, aircraft control and automotive engine control. A great number of excellent papers are devoted to this field [8-10]. Switched neutral systems have strong engineering background in network control [11] and circuit systems [12]. The complicated solution behavior of switched neutral systems makes the study a challenging task [13-14]. It is well understood that adoption of multiple Lyapunov functionals often gives rise to less conservative stability * This work was supported by the National Nature Science Foundation of China under Grants 61174073 and 90816028, and the Fundamental Research Funds for the Central Universities under Grant N090604003. and by Ministry of Education & Science of R. Macedonia (Grant 14-3154/1-17.12.2007) and Dogus University Fund for Science. conditions in the switched system area. It has been considered as an important analysis tool. The traditional multiple Lyapunov functionals method requires the nonincreasing conditions on the connecting adjacent Lyapunov functionals at switching points [8] [15]. The nonincreasing condition is conservative. In [10], a multiple generalized Lyapunov functionals method is presented to break this monotony, which allows the increasing on the connecting adjacent Lyapunov functionals at switching points. In this way, stability, -gain and 2 L H ∞ control for a class of nonlinear switched systems are discussed in there. On the other hand, sliding modes or chattering are often undesirable in practical systems due to the very fast switching which causes excessive equipment wear. The hysteresis switching, which can avoid sliding modes and chattering, is very effective in control design [16-18]. In this paper, we study the stability of a class of switched neutral systems with discrete time-varying delays. It is no need to require any stability property associate with each individual subsystem. By employing the multiple generalized Lyapunov functionals method and a free weighting matrix technique, a delay-dependent stability condition is developed under a hysteresis switching law. The organization of this paper is as follows. Section 2 gives problem formulations and preliminaries. Section 3 gives the main results. A simulation example is presented in Section 4 and Section 5 gives the conclusions.