Automatica 46 (2010) 2100–2104 Contents lists available at ScienceDirect Automatica journal homepage: www.elsevier.com/locate/automatica Technical communique A new result on stability analysis for stochastic neutral systems ✩ Yun Chen a,b , Wei Xing Zheng b,∗ , Anke Xue a a Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China b School of Computing and Mathematics, University of Western Sydney, Penrith South DC NSW 1797, Australia article info Article history: Received 26 November 2009 Received in revised form 24 June 2010 Accepted 16 July 2010 Available online 31 August 2010 Keywords: Stochastic neutral systems Mean-square exponential stability Delay-dependent criterion Generalized Finsler lemma abstract This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Dynamical systems modeled by neutral functional differential equations are generally called neutral systems in the literature. The study of neutral systems has received considerable attention during the past few decades (see, e.g., Gu, Kharitonov, and Chen (2003), Han (2002), He, Wu, She, and Liu (2004), Li and Liu (2009) and Suplin, Fridman, and Shaked (2006) and the references therein). Recently, increasing efforts have been made to investigate stochastic retarded/neutral systems, since stochastic perturbations exist in many real-world systems (Mao, 1997). It is noticed that the methods in Gao, Lam, and Wang (2006), Wang and Ho (2003) and Xu, Shi, Chu, and Zou (2006) are delay-independent, so they may be restrictive, especially when the delays are small. In order to reduce the conservatism, the delay-dependent stability for stochastic systems was studied in Basin and Rodkina (2008), Chen, Guan, and Lu (2005), Chen, Xue, Zhou, and Lu (2008), Chen, Zheng, and Shen (2009), Huang and Mao (2009), Rodkina and Basin (2006, 2007) and Yue and Han (2005), respectively. Thereinto, the model ✩ This work was supported partially by the National Basic Research Program of China (973 Program) under grant 2009CB320602 the National Natural Science Foundation of China under grants 60974006, 60974138, the Zhejiang Provincial Natural Science Foundation of China under grant Y1090465, and by a research grant from the Australian Research Council. This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Keqin Gu under the direction of Editor André L. Tits. ∗ Corresponding author. Tel.: +61 2 4736 0608; fax: +61 2 4736 0867. E-mail addresses: cloudscy@hdu.edu.cn (Y. Chen), w.zheng@uws.edu.au (W.X. Zheng), akxue@hdu.edu.cn (A. Xue). transformation method together with bounding techniques for cross-terms were extended to consider the stability of stochastic linear delay systems (Chen et al., 2005). Resorting to some slack matrix variables, delay-dependent results were obtained in Chen et al. (2008) and Yue and Han (2005). Based on the free-weighting matrix technique, the mean-square exponential stability for stochastic delay systems of neutral type was studied in Chen et al. (2009) and Huang and Mao (2009). In addition, the almost sure exponential stability of stochastic neutral systems was also discussed in Huang and Mao (2009). Moreover, for nonlinear stochastic neutral systems, various delay-dependent stability results were obtained in Basin and Rodkina (2008) and Rodkina and Basin (2006, 2007). However, model transformations may lead to additional dynamics of the original systems (see Gu et al., 2003), and cross- term bounding techniques can bring conservatism. Moreover, as pointed out by Xu and Lam (2007), in some cases free matrix variables may not be useful to the reduction of conservatism. Besides, those variables will increase the computational burden and make it rather difficult to synthesize systems. Therefore, there is a need to establish some new stability results with less conservatism and lower computational cost such that the design purposes can be achieved more easily. The above consideration has motivated the present work. This paper focuses on the stability analysis of linear stochas- tic neutral-type systems. By Lyapunov–Krasovskii functional the- ory, a new delay-dependent mean-square exponential stability criterion is formulated in terms of linear matrix inequality (LMI). The presented condition is simple and efficient, because none of the model transformations, bounding techniques for cross-terms 0005-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.automatica.2010.08.007