Passive stability and synchronization of complex spatio-temporal switching networks with time delays

In this paper, a new model of complex spatio-temporal switching network is established. Each subsystem of the network at a different time interval corresponds to a different switching mode. Switching the signal depends on both the instant time t and the index of node i. Based on passivity property, the passive stability and synchronization of this kind of network with time delays are taken into account. An example and simulation results are included.

[1]  Changsong Zhou,et al.  Universality in the synchronization of weighted random networks. , 2006, Physical review letters.

[2]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[3]  Chun-Guang Li,et al.  Passivity Analysis of Neural Networks With Time Delay , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[4]  B. Brogliato,et al.  Dissipative Systems Analysis and Control , 2000 .

[5]  Beom Jun Kim,et al.  Synchronization on small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  D. Angeli,et al.  Extension of a result by Moreau on stability of leaderless multi-agent systems. , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  Xiaofeng Liao,et al.  Synchronization in coupled map lattices with small-world delayed interactions , 2004 .

[8]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[9]  Emilia Fridman,et al.  On delay-dependent passivity , 2002, IEEE Trans. Autom. Control..

[10]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[11]  Juebang Yu,et al.  Synchronization in small-world oscillator networks with coupling delays , 2004 .

[12]  M. Mahmoud,et al.  Passivity and passification of time-delay systems , 2004 .

[13]  Xiaofan Wang,et al.  On synchronization in scale-free dynamical networks , 2005 .

[14]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[15]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[16]  Jürgen Kurths,et al.  Synchronization of complex dynamical networks with time delays , 2006 .

[17]  Chunguang Li,et al.  Local stability and Hopf bifurcation in small-world delayed networks , 2004 .

[18]  Rogelio Lozano,et al.  On the passivity of linear delay systems , 2001, IEEE Trans. Autom. Control..

[19]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.

[20]  Zhi-Hong Guan,et al.  Synchronization of Complex Dynamical Networks with Switching Topology via Adaptive Control , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[21]  M. G. Earl,et al.  Synchronization in oscillator networks with delayed coupling: a stability criterion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Xin-She Yang,et al.  Fractals in small-world networks with time-delay , 2002, 1003.4949.

[23]  Guanrong Chen,et al.  Novel criteria of synchronization stability in complex networks with coupling delays , 2007 .

[24]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

[25]  Béla Bollobás,et al.  Random Graphs , 1985 .

[26]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[27]  Xiaofeng Liao,et al.  Passivity and Passification of Fuzzy Systems with Time Delays , 2006, Comput. Math. Appl..

[28]  M. Spong,et al.  Agreement with non-uniform information delays , 2006, 2006 American Control Conference.

[29]  S. Strogatz,et al.  Time Delay in the Kuramoto Model of Coupled Oscillators , 1998, chao-dyn/9807030.

[30]  P. Arena,et al.  Cellular neural networks: a paradigm for nonlinear spatio-temporal processing , 2001 .

[31]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .