Synchronization of directed switched complex networks with stochastic link perturbations and mixed time-delays

Abstract In this paper, the synchronization problem is studied for a class of directed switched complex networks. The links among the nodes are perturbed by stochastic noises and the topology varies according to certain predetermined switching rules. The coupled networks under consideration are subject to mixed delays comprising both discrete and distributed ones. A new estimate of the general algebraic connectivity is firstly given for the directed complex networks, based on which the exponential synchronization problem is analyzed by virtue of the average-dwell-time technique. Then, sufficient conditions are derived to guarantee the synchronization in mean square provided that the switching is slow on the average. Subsequently, the switched complex networks with link failures are investigated and it is shown that the synchronization can be achieved if the average link failure ratio does not exceed certain threshold. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed algorithm.

[1]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[2]  Tingwen Huang,et al.  Passivity-based synchronization of a class of complex dynamical networks with time-varying delay , 2015, Autom..

[3]  Seiichi Nakamori,et al.  Signal estimation with multiple delayed sensors using covariance information , 2010, Digit. Signal Process..

[4]  Deborah Chasman,et al.  Network-based approaches for analysis of complex biological systems. , 2016, Current opinion in biotechnology.

[5]  Eckehard Schöll,et al.  Synchronization and control in time-delayed complex networks and spatio-temporal patterns , 2016 .

[6]  Guanghui Wen,et al.  Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[8]  Mario di Bernardo,et al.  Novel decentralized adaptive strategies for the synchronization of complex networks , 2009, Autom..

[9]  Raquel Caballero-Águila,et al.  Linear estimation based on covariances for networked systems featuring sensor correlated random delays , 2013, Int. J. Syst. Sci..

[10]  Wenwu Yu,et al.  Impulsive synchronization schemes of stochastic complex networks with switching topology: Average time approach , 2014, Neural Networks.

[11]  Lei Guo,et al.  Stability analysis of impulsive parabolic complex networks with multiple time-varying delays , 2012, Neurocomputing.

[12]  Graziano Chesi,et al.  LMI Techniques for Optimization Over Polynomials in Control: A Survey , 2010, IEEE Transactions on Automatic Control.

[13]  Andrew Quinn,et al.  Social Network Analysis for Analyzing Groups as Complex Systems , 2012 .

[14]  Jun Zhao,et al.  Exponential Synchronization of Complex Delayed Dynamical Networks With Switching Topology , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Wenwu Yu,et al.  Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[17]  Florian Dörfler,et al.  Synchronization in complex networks of phase oscillators: A survey , 2014, Autom..

[18]  Karl Henrik Johansson,et al.  Event-triggered pinning control of complex networks with switching topologies , 2014, 53rd IEEE Conference on Decision and Control.

[19]  Haitao Liu,et al.  Approaching human language with complex networks. , 2014, Physics of life reviews.

[20]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Michael V. Basin,et al.  Optimal control for linear systems with multiple time delays in control input , 2006, IEEE Transactions on Automatic Control.

[22]  Yurong Liu,et al.  Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects , 2016, Neurocomputing.

[23]  Jing Zhu,et al.  Fundamental Limits on Uncertain Delays: When Is a Delay System Stabilizable by LTI Controllers? , 2017, IEEE Transactions on Automatic Control.

[24]  Hamid Reza Karimi,et al.  Passivity-based output feedback control of Markovian jump systems with discrete and distributed time-varying delays , 2013, Int. J. Syst. Sci..

[25]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[26]  Peng Shi,et al.  Central Suboptimal H∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay , 2009, Circuits Syst. Signal Process..

[27]  Miguel Lurgi,et al.  The effects of space and diversity of interaction types on the stability of complex ecological networks , 2015, Theoretical Ecology.

[28]  Yonggang Chen,et al.  Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback , 2015, Autom..

[29]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent H∞ filtering for complex dynamical networks with time-varying delays in nonlinear function and network couplings , 2016, Signal Process..

[30]  Lei Wang,et al.  Synchronization in complex networks with switching topology , 2011 .

[31]  Wenwu Yu,et al.  Distributed Adaptive Control of Synchronization in Complex Networks , 2012, IEEE Transactions on Automatic Control.

[32]  Keith J. Burnham,et al.  On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters , 2002, IEEE Trans. Autom. Control..

[33]  Julio M. Ottino,et al.  Complex systems and networks: Challenges and opportunities for chemical and biological engineers , 2004 .