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A new result on stability analysis for stochastic neutral systems. (English) Zbl 1205.93160
Summary: 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.

MSC:
93E15 Stochastic stability in control theory
93C05 Linear systems in control theory
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[1] Basin, M.V.; Rodkina, A.E., On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays, Nonlinear analysis, 68, 2147-2157, (2008) · Zbl 1154.34044
[2] Chen, W.-H.; Guan, Z.-H.; Lu, X., Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach, Systems & control letters, 54, 547-555, (2005) · Zbl 1129.93547
[3] Chen, Y.; Xue, A.; Zhou, S.; Lu, R., Delay-dependent robust control for uncertain stochastic time-delay systems, Circuits, systems & signal processing, 27, 447-460, (2008) · Zbl 1179.93169
[4] Chen, W.-H.; Zheng, W.X.; Shen, Y., Delay-dependent stochastic stability and \(H_\infty\)-control of uncertain neutral stochastic systems with time delay, IEEE transactions on automatic control, 54, 1660-1667, (2009) · Zbl 1367.93694
[5] Coutinho, D.F.; de Souza, C.E., Delay-dependent robust stability and \(L_2\)-gain analysis of a class of nonlinear time-delay systems, Automatica, 44, 2006-2018, (2008) · Zbl 1283.93219
[6] Du, B.; Lam, J.; Shu, Z.; Wang, Z., A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components, IET control theory & applications, 3, 383-390, (2009)
[7] Gao, H.; Lam, J.; Wang, C., Robust energy-to-peak filter design for stochastic time-delay systems, Systems & control letters, 55, 101-111, (2006) · Zbl 1129.93538
[8] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Boston · Zbl 1039.34067
[9] Han, Q.-L., Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723, (2002) · Zbl 1020.93016
[10] He, Y.; Wu, M.; She, J.-H.; Liu, G.-P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems & control letters, 51, 57-65, (2004) · Zbl 1157.93467
[11] Huang, L.; Mao, X., Delay-dependent exponential stability of neutral stochastic delay systems, IEEE transactions on automatic control, 54, 147-152, (2009) · Zbl 1367.93511
[12] Li, M.; Liu, L., A delay-dependent stability criterion for linear neutral delay systems, Journal of the franklin institute, 346, 33-37, (2009) · Zbl 1298.34153
[13] Mao, X., Stochastic differential equations and their applications, (1997), Horwood Publishing Chichester
[14] Qiu, J.; Feng, G.; Yang, J., A new design of delay-dependent robust \(H_\infty\) filtering for discrete-time T-S fuzzy systems with time-varying delay, IEEE transactions on fuzzy systems, 17, 1044-1058, (2009)
[15] Rodkina, A.E.; Basin, M.V., On delay-dependent stability for a class of nonlinear stochastic delay-differential equations, Mathematics of control, signals, and systems, 18, 187-197, (2006) · Zbl 1103.93043
[16] Rodkina, A.E.; Basin, M.V., On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term, Systems & control letters, 56, 423-430, (2007) · Zbl 1124.93066
[17] Suplin, V.; Fridman, E.; Shaked, U., \(H_\infty\) control of linear uncertain time-delay systems—a projection approach, IEEE transactions on automatic control, 51, 680-685, (2006) · Zbl 1366.93163
[18] Wang, Z.; Ho, D.W.C., Filtering on nonlinear time-delay stochastic systems, Automatica, 39, 101-109, (2003) · Zbl 1010.93099
[19] Xu, S.; Lam, J., On equivalence and efficiency of certain stability criteria for time-delay systems, IEEE transactions on automatic control, 52, 95-101, (2007) · Zbl 1366.93451
[20] Xu, S.; Shi, P.; Chu, Y.; Zou, Y., Robust stochastic stabilization and \(H_\infty\) control of uncertain neutral stochastic time-delay systems, Journal of mathematical analysis and applications, 314, 1-16, (2006) · Zbl 1127.93053
[21] Yue, D.; Han, Q.-L., Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching, IEEE transactions on automatic control, 50, 217-222, (2005) · Zbl 1365.93377
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