Synchronization of a delayed complex dynamical network with free coupling matrix

This paper considers synchronization problem of a delayed complex dynamical network. For the problem, the virtual target node is chosen as one of nodes in the complex network. It should be pointed out that only one connection is needed between a real target node and a virtual target node instead of N connections. Moreover, the proposed synchronization scheme does not require additional conditions for coupling matrix unlike the existing works. Based on Lyapunov stability theory, a new design criterion for an adaptive feedback controller to achieving synchronization between the real target node and all nodes of the delayed complex network is developed. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

[1]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

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

[3]  Liang Chen,et al.  Adaptive synchronization between two complex networks with nonidentical topological structures , 2008 .

[4]  Hamid Reza Karimi,et al.  Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations , 2011 .

[5]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[6]  Degang Xu,et al.  Synchronization criterions and pinning control of general complex networks with time delay , 2009, Appl. Math. Comput..

[7]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[8]  Jin Bae Park,et al.  Adaptive Output Feedback Control of Flexible-Joint Robots Using Neural Networks: Dynamic Surface Design Approach , 2008, IEEE Transactions on Neural Networks.

[9]  D. H. Ji,et al.  Synchronization of singular complex dynamical networks with time-varying delays , 2010, Appl. Math. Comput..

[10]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[11]  Zhisheng Duan,et al.  Study of delay-independent decentralized guaranteed cost control for large scale systems , 2011 .

[12]  Shengyuan Xu,et al.  Further results on adaptive robust control of uncertain time-delay systems , 2008 .

[13]  Junan Lu,et al.  Structure identification of uncertain general complex dynamical networks with time delay , 2009, Autom..

[14]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[15]  Choon Ki Ahn.  H∞ Chaos synchronization for nonlinear Bloch equations , 2009 .

[16]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[17]  Albert C. J. Luo,et al.  A theory for synchronization of dynamical systems , 2009 .

[18]  T. Liao,et al.  H∞ synchronization of chaotic systems using output feedback control design , 2007 .

[19]  Shengyuan Xu,et al.  Robust admissibility of time-varying singular systems with commensurate time delays , 2009, Autom..

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

[21]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

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

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

[24]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[25]  Jinde Cao,et al.  Synchronization of complex dynamical networks with nonidentical nodes , 2010 .

[26]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[27]  Daewon Kim,et al.  Task Assignment Strategies for a Complex Real-time Network System , 2006 .

[28]  Song Zheng,et al.  Adaptive projective synchronization in complex networks with time-varying coupling delay , 2009 .

[29]  Youxian Sun,et al.  Adaptive synchronization of weighted complex dynamical networks through pinning , 2008 .

[30]  Linying Xiang,et al.  On pinning synchronization of general coupled networks , 2011 .

[31]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

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