Passivity analysis of complex dynamical networks with multiple time-varying delays

We investigate input passivity and output passivity for a generalized complex network with non-linear, time-varying, non-symmetric and delayed coupling. By constructing some suitable Lyapunov functionals, several sufficient conditions ensuring input passivity and output passivity are derived for complex dynamical networks. Finally, two numerical examples are given to show the effectiveness of the obtained results.

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

[2]  Beom Jun Kim,et al.  Factors that predict better synchronizability on complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Raymond Gorez,et al.  Passivity approach to fuzzy control systems , 1998, at - Automatisierungstechnik.

[4]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[5]  L. Chua.  Passivity and complexity , 1999 .

[6]  Zengqiang Chen,et al.  Pinning control of complex dynamical networks with heterogeneous delays , 2008, Comput. Math. Appl..

[7]  Gang Feng,et al.  Controlling complex dynamical networks with coupling delays to a desired orbit , 2006 .

[8]  Qiankun Song,et al.  Passivity analysis of discrete-time stochastic neural networks with time-varying delays , 2009, Neurocomputing.

[9]  Xiaoqun Wu.  Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay , 2008 .

[10]  Huijun Gao,et al.  Passivity and Passification for Networked Control Systems , 2007, SIAM J. Control. Optim..

[11]  Yan-Wu Wang,et al.  Robust Stabilization of Complex Switched Networks With Parametric Uncertainties and Delays Via Impulsive Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  Xuyang Lou,et al.  Passivity analysis of integro-differential neural networks with time-varying delays , 2007, Neurocomputing.

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

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

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

[16]  Enric Fossas,et al.  Feedback passivity of nonlinear discrete-time systems with direct input-output link, , 2004, Autom..

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

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

[19]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[20]  Chong Lin,et al.  Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays ☆ , 2009 .

[21]  Ju H. Park.  Further results on passivity analysis of delayed cellular neural networks , 2007 .

[22]  Adilson E Motter,et al.  Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? , 2003, Physical review letters.

[23]  Xingwen Liu,et al.  Passivity analysis of uncertain fuzzy delayed systems , 2007 .

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

[25]  Eva M. Navarro-López,et al.  Several dissipativity and passivity implications in the linear discrete-time setting , 2005 .

[26]  Huey-Jian Uang,et al.  On the dissipativity of nonlinear systems: Fuzzy control approach , 2005, Fuzzy Sets Syst..

[27]  Wen Yu.  Passive equivalence of chaos in Lorenz system , 1999 .

[28]  Jun Zhao,et al.  Passivity and stability of switched systems: A multiple storage function method , 2008, Syst. Control. Lett..

[29]  Li Lee,et al.  Passivity approach to feedback connection stability for discrete-time descriptor systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[30]  Pei-Hwa Huang,et al.  Fuzzy controller design for passive continuous-time affine T-S fuzzy models with relaxed stability conditions. , 2009, ISA transactions.

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

[32]  Jun-an Lu,et al.  Topology identification of weighted complex dynamical networks , 2007 .

[33]  Lihua Xie,et al.  Passivity analysis and passification for uncertain signal processing systems , 1998, IEEE Trans. Signal Process..

[34]  Huai-Ning Wu,et al.  Passivity analysis of impulsive complex networks , 2011, Int. J. Autom. Comput..

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

[36]  Qiankun Song,et al.  New results on passivity analysis of uncertain neural networks with time-varying delays , 2010, Int. J. Comput. Math..

[37]  Mao-Yin Chen,et al.  Synchronization in Complex Dynamical Networks With Random Sensor Delay , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  Zengrong Liu,et al.  Robust impulsive synchronization of complex delayed dynamical networks , 2008 .

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

[40]  Jin-Liang Wang,et al.  Local and global exponential output synchronization of complex delayed dynamical networks , 2012 .

[41]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[42]  Glenn Vinnicombe,et al.  Scalable robust stability for nonsymmetric heterogeneous networks , 2007, Autom..

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

[44]  C. Wu.  Synchronization in arrays of coupled nonlinear systems: passivity, circle criterion, and observer design , 2001 .

[45]  David J. Hill,et al.  Passivity-based control and synchronization of general complex dynamical networks , 2009, Autom..

[46]  Wenlian Lu,et al.  Synchronization of Discrete-Time Dynamical Networks with Time-Varying Couplings , 2008, SIAM J. Math. Anal..

[47]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[48]  Tingwen Huang,et al.  Local and global exponential synchronization of complex delayed dynamical networkswith general topology , 2011 .

[49]  Zengqiang Chen,et al.  Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers , 2008, Science in China Series F: Information Sciences.

[50]  Alan J. Laub,et al.  Matrix analysis - for scientists and engineers , 2004 .

[51]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[52]  Guanrong Chen,et al.  Global synchronization and asymptotic stability of complex dynamical networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[53]  Shihua Chen,et al.  Global synchronization of nonlinearly coupled complex networks with non-delayed and delayed coupling , 2010 .

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

[55]  Guanrong Chen,et al.  Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint , 2003 .

[56]  Zhi-Hong Guan,et al.  Passive stability and synchronization of complex spatio-temporal switching networks with time delays , 2009, Autom..

[57]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.