Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching

Authors: Xia Zhou, Shouming Zhong

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, Itˆo 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.

Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078609

References:

[1] Pecora LM. synchronization in chaotic systems. Phys Rev Lett 1991;64:821-24.
[2] H.M.Guo, S.M.Zhong. Synchronization criteria of time-delay feedback control system with sector-bounded nonlinearity. Applied Mathematics and Computation 2007;191:550-9.
[3] Z.M.Ge, J.K.Lee. Chaos synchronization and parameter identification for gyroscope system. Applied Mathematics and Computation 2005;163:667- 82.
[4] Z.X. Liu, S.L, S.M.Zhong, M.Ye.pth moment exponential synchronization analysis for a class of stochastic neural networks with mixed delays. Communications in Nonlinear Science and Numerical Simulation. 2010;15:1899-1909.
[5] X.Z.Gao, S.M.Zhong, Fengyin Gao. Exponential synchronization of neural networks with time-varying delays. Nonlinear Analysis: Theory, Methods and Applications. 2009;71:2003-11.
[6] H.M. Guo, S.M.Zhong, F.Y.Gao. Design of PD controller for master-slave synchronization of Lur-e systems with time-delay. Applied Mathematics and Computation. 2009;212:86-93.
[7] H.H.Chen. Global synchronization of chaotic systems via linear balanced feedback control. Applied Mathematics and Computation 2007;186:923- 31.
[8] B.Wang, G.J.Wen. On the synchronization of uncertain masterCslave chaotic systems with disturbance. Chaos, Solitons and Fractals. 2009;41:145-51.
[9] X.C.Li, W.Xu, R.H.Li. Chaos synchronization of the energy resource system. Chaos, Solitons and Fractals 2009;40:642-52.
[10] C.F.Huang, K.H.Cheng, J.J.Yan. Robust chaos synchronization of fourdimensional energy resource systems subject to unmatched uncertainties, Commun Nonlinear Sci Numer Simulat 2009;14:2784-92.
[11] X.F.Wu, J.P.Cai, M.H.Wang. Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control. Chaos, Solitons and Fractals 2008;36:121-8.
[12] Yalicn ME, Suykens JAK, Vandewallw J. Master-slave synchronization of Lur-e systems with time-delay, Int J Bifur Chaos 2001;11:1707-22.
[13] J.D.Cao, H.X. Li, Daniel W.Ho. Synchronization criteria of Lur-e systems with time-delay feedback control. Chaos, Solitons and Fractals 2005;23:1285-98.
[14] J.Xiang, Y.J.Li, W.Wei. An improved condition for masterCslave synchronization of Lure systems with time delay. Physics Letters A 2007;362:154-8.
[15] T.Li, J.J.Yu, Z.Wang. Delay-range-dependent synchronization ruiterion for Lur-e systems with delay feedback control. Commun Nonlinear Sci Numer Simulat 2009;14:1796-803.
[16] X.R.Mao. Exponential stability of stochastic delay interval systems with Markonvain switching. IEEE Transactions on Automatic Control. 2002;47:1604-12.