Delay-dependent synchronization for non-diffusively coupled time-varying complex dynamical networks

This paper investigates the delay-dependent synchronization schemes for the non-diffusively coupled time-varying complex dynamical networks. The outer coupling configuration matrix in our network model may be non-diffusive, time-varying, uncertain, asymmetric and irreducible. Different time-varying coupling delays for different nodes are also put into consideration in this paper. Besides, the nodes may have different state dimensions. Furthermore, only the common bound of the outer coupling coefficients (CBOCC) is used to design the synchronization controllers. If the CBOCC is known, our delay-dependent synchronization scheme can guarantee the network achieving exponential synchronization. And when the CBOCC is uncertain, the adaptive synchronization scheme, where only one adaptive law is needed, is proposed to guarantee the network realizing asymptotic synchronization. Simulation examples are provided to verify the effectiveness and feasibility of our theoretical results.

[1]  Yong He,et al.  Stability Analysis and Robust Control of Time-Delay Systems , 2010 .

[2]  E. Ruiz-Velazquez,et al.  Synchronization in complex networks with distinct chaotic nodes , 2009 .

[3]  Mario di Bernardo,et al.  On QUAD, Lipschitz, and Contracting Vector Fields for Consensus and Synchronization of Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Hongtao Lu,et al.  Outer synchronization of uncertain general complex delayed networks with adaptive coupling , 2012, Neurocomputing.

[5]  Lili Zhang,et al.  Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers , 2013, Int. J. Control.

[6]  Hao Shen,et al.  Robust extended dissipative control for sampled-data Markov jump systems , 2014, Int. J. Control.

[7]  Jinde Cao,et al.  Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations , 2014, Appl. Math. Comput..

[8]  Guanrong Chen,et al.  Synchronization in a class of weighted complex networks with coupling delays , 2008 .

[9]  Ju H. Park,et al.  Finite-time synchronization control for uncertain Markov jump neural networks with input constraints , 2014, Nonlinear Dynamics.

[10]  Ju H. Park,et al.  Integral control for synchronization of complex dynamical networks with unknown non-identical nodes , 2013, Appl. Math. Comput..

[11]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[12]  P DeLellis,et al.  Synchronization and control of complex networks via contraction, adaptation and evolution , 2010, IEEE Circuits and Systems Magazine.

[13]  Juan Gonzalo Barajas-Ramírez,et al.  Synchronization in complex networks under structural evolution , 2014, J. Frankl. Inst..

[14]  Song Zheng.  Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling , 2012 .

[15]  Wenwu Yu,et al.  Adaptive cluster synchronization in networks with time-varying and distributed coupling delays , 2014 .

[16]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[17]  Ju H. Park,et al.  Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control , 2012, Appl. Math. Comput..

[18]  K. Sudheer,et al.  Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters , 2009 .

[19]  Jun Zhao,et al.  Global Bounded Synchronization of General Dynamical Networks With Nonidentical Nodes , 2012, IEEE Transactions on Automatic Control.

[20]  Ju H. Park,et al.  Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays , 2012, Appl. Math. Comput..

[21]  Chen Guan-Rong,et al.  Cost and Effects of Pinning Control for Network Synchronization , 2007, ArXiv.

[22]  Jinde Cao,et al.  Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems , 2013 .

[23]  Yun Zhang,et al.  The synchronization of complex dynamical networks with similar nodes and coupling time-delay , 2013, Appl. Math. Comput..

[24]  Y.-H. Wang,et al.  Robust control for nonlinear similar composite systems with uncertain parameters , 2000 .

[25]  Yun Zhang,et al.  Stabilization and Synchronization of Complex Dynamical Networks With Different Dynamics of Nodes Via Decentralized Controllers , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  Hongjie Li,et al.  Synchronization and state estimation for singular complex dynamical networks with time-varying delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[27]  Shengyuan Xu,et al.  Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays , 2012, J. Frankl. Inst..

[28]  Ju H. Park,et al.  Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control , 2012, Appl. Math. Comput..

[29]  Zhang Yi,et al.  Synchronization analysis of delayed complex networks with time-varying couplings , 2008 .

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

[31]  W. K. Wong,et al.  Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties , 2012 .

[32]  Siying Zhang,et al.  Synchronization for Time‐Delayed Coupling Complex Dynamic Networks with Different Dimensional Nodes Via Decentralized Dynamic Compensation Controllers , 2015 .

[33]  Ju H. Park,et al.  On synchronization criterion for coupled discrete-time neural networks with interval time-varying delays , 2013, Neurocomputing.