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Exponential stability analysis for uncertain switched neutral systems with interval-time-varying state delay. (English) Zbl 1192.34085
Summary: The global exponential stability for a class of switched neutral systems with interval-time-varying state delay and two classes of perturbations is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee exponential stability for our considered systems under any switched signal. The Razumikhin-like approach and the Leibniz-Newton formula are used to find the stability conditions. Structured and unstructured uncertainties are studied in this paper. Finally, some numerical examples are illustrated to show the improved results from using this method.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K40 Neutral functional-differential equations 34A36 Discontinuous ordinary differential equations
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##### References:
 [1] Sun, X.M.; Wang, W.; Liu, G.P.; Zhao, J., Stability analysis for linear switched systems with time-varying delay, IEEE trans. syst. man cybern. (B), 38, 528-5533, (2008) [2] Liu, J.; Liu, X.; Xie, W.C., Delay-dependent robust control for uncertain switched systems with time-delay, Nonlinear anal. hybrid syst., 2, 81-95, (2008) · Zbl 1157.93362 [3] Sun, Y.G.; Wang, L.; Xie, G., Stability of switched systems with time-varying delays: delay-dependent common Lyapunov functional approach, Proc. amer. control conf., 5, 1544-1549, (2006) [4] C.H. Wang, L.X. Zhang, H.J. Gao, L.G. Wu, Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems, in: Proc. 4th Int. Conf. Mach. Learn. Cybern., Guangzhou, 2005, pp. 18-21 [5] Sun, X.M.; Zhao, J.; Hill, D.J., Stability and $$L_2$$-gain analysis for switched delay systems: A delay-dependent method, Automatica, 42, 1769-1774, (2006) · Zbl 1114.93086 [6] Kim, S.; Campbell, S.A.; Liu, X., Stability of a class of linear switching systems with time delay, IEEE trans. circuits syst. (I), 53, 384-393, (2006) · Zbl 1374.94950 [7] Liu, D.; Liu, X.; Zhong, S., Delay-dependent robust stability and control synthesis for uncertain switched neutral systems with mixed delays, Appl. math. comput., 202, 828-839, (2008) · Zbl 1143.93020 [8] Zhang, Y.; Liu, X.; Zhu, H.; Zhong, S., Stability analysis and control synthesis for a class of switched neutral systems, Appl. math. comput., 190, 1258-1266, (2007) · Zbl 1117.93062 [9] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Boston, Massachusetts · Zbl 1039.34067 [10] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002 [11] Kolmanovskii, V.B.; Myshkis, A., Applied theory of functional differential equations, (1992), Kluwer Academic Publishers Netherlands [12] Lien, C.H.; Yu, K.W.; Lin, Y.F.; Chung, Y.J.; Chung, L.Y., Exponential convergence rate estimation for uncertain delayed neural networks of neutral type, Chaos solitons fractals, (2007) [13] Yu, K.W.; Lien, C.H., Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos solitons fractals, 38, 650-657, (2008) · Zbl 1146.93366 [14] Boyd, S.; Ghaoui, LE; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004
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