{"title":"Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching","authors":"Xia Zhou, Shouming Zhong","volume":39,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":407,"pagesEnd":413,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12126","abstract":"
The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, It\u2566åo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.<\/p>\r\n","references":"[1] Pecora LM. synchronization in chaotic systems. Phys Rev Lett\r\n1991;64:821-24.\r\n[2] H.M.Guo, S.M.Zhong. Synchronization criteria of time-delay feedback\r\ncontrol system with sector-bounded nonlinearity. Applied Mathematics\r\nand Computation 2007;191:550-9.\r\n[3] Z.M.Ge, J.K.Lee. Chaos synchronization and parameter identification for\r\ngyroscope system. Applied Mathematics and Computation 2005;163:667-\r\n82.\r\n[4] Z.X. Liu, S.L, S.M.Zhong, M.Ye.pth moment exponential synchronization\r\nanalysis for a class of stochastic neural networks with mixed\r\ndelays. Communications in Nonlinear Science and Numerical Simulation.\r\n2010;15:1899-1909.\r\n[5] X.Z.Gao, S.M.Zhong, Fengyin Gao. Exponential synchronization of\r\nneural networks with time-varying delays. Nonlinear Analysis: Theory,\r\nMethods and Applications. 2009;71:2003-11.\r\n[6] H.M. Guo, S.M.Zhong, F.Y.Gao. Design of PD controller for master-slave\r\nsynchronization of Lur-e systems with time-delay. Applied Mathematics\r\nand Computation. 2009;212:86-93.\r\n[7] H.H.Chen. Global synchronization of chaotic systems via linear balanced\r\nfeedback control. Applied Mathematics and Computation 2007;186:923-\r\n31.\r\n[8] B.Wang, G.J.Wen. On the synchronization of uncertain masterCslave\r\nchaotic systems with disturbance. Chaos, Solitons and Fractals.\r\n2009;41:145-51.\r\n[9] X.C.Li, W.Xu, R.H.Li. Chaos synchronization of the energy resource\r\nsystem. Chaos, Solitons and Fractals 2009;40:642-52.\r\n[10] C.F.Huang, K.H.Cheng, J.J.Yan. Robust chaos synchronization of fourdimensional\r\nenergy resource systems subject to unmatched uncertainties,\r\nCommun Nonlinear Sci Numer Simulat 2009;14:2784-92.\r\n[11] X.F.Wu, J.P.Cai, M.H.Wang. Global chaos synchronization of the parametrically\r\nexcited Duffing oscillators by linear state error feedback\r\ncontrol. Chaos, Solitons and Fractals 2008;36:121-8.\r\n[12] Yalicn ME, Suykens JAK, Vandewallw J. Master-slave synchronization\r\nof Lur-e systems with time-delay, Int J Bifur Chaos 2001;11:1707-22.\r\n[13] J.D.Cao, H.X. Li, Daniel W.Ho. Synchronization criteria of Lur-e\r\nsystems with time-delay feedback control. Chaos, Solitons and Fractals\r\n2005;23:1285-98.\r\n[14] J.Xiang, Y.J.Li, W.Wei. An improved condition for masterCslave\r\nsynchronization of Lure systems with time delay. Physics Letters A\r\n2007;362:154-8.\r\n[15] T.Li, J.J.Yu, Z.Wang. Delay-range-dependent synchronization ruiterion\r\nfor Lur-e systems with delay feedback control. Commun Nonlinear Sci\r\nNumer Simulat 2009;14:1796-803.\r\n[16] X.R.Mao. Exponential stability of stochastic delay interval systems\r\nwith Markonvain switching. IEEE Transactions on Automatic Control.\r\n2002;47:1604-12.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 39, 2010"}