Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching
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.
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[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-
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[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61159", author = "Xia Zhou and Shouming Zhong", title = "Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching", 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.", volume = "4", number = "3", pages = "411-6", }
