Passivity of linearly coupled reaction-diffusion neural networks with switching topology and time-varying delay

This paper studies the passivity of a general array model of coupled reaction-diffusion neural networks (CRDNNs) with switching topology and time-varying delay. By exploiting the Lyapunov functional method and some inequality techniques, several sufficient criteria are established to ensure the input strict passivity and output strict passivity of the proposed network model. Moreover, we reveal the relationship between passivity and stability of CRDNNs. Based on the obtained passivity results and relationship between passivity and stability, a synchronization criterion is presented for CRDNNs. Finally, two numerical examples are provided to demonstrate the correctness and effectiveness of the theoretical results.

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

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

[3]  Huaguang Zhang,et al.  Near-Optimal Control for Nonzero-Sum Differential Games of Continuous-Time Nonlinear Systems Using Single-Network ADP , 2013, IEEE Transactions on Cybernetics.

[4]  Jinde Cao,et al.  Synchronization-based approach for parameters identification in delayed chaotic neural networks , 2007 .

[5]  Jan C. Willems,et al.  Dissipative Dynamical Systems , 2007, Eur. J. Control.

[6]  Tiedong Ma,et al.  Synchronization of multi-agent stochastic impulsive perturbed chaotic delayed neural networks with switching topology , 2015, Neurocomputing.

[7]  Tingwen Huang,et al.  Passivity and Synchronization of Linearly Coupled Reaction-Diffusion Neural Networks With Adaptive Coupling , 2015, IEEE Transactions on Cybernetics.

[8]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[9]  Jinde Cao,et al.  Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control , 2014, Neurocomputing.

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

[11]  Xiwei Liu,et al.  Synchronization of linearly coupled neural networks with reaction-diffusion terms and unbounded time delays , 2010, Neurocomputing.

[12]  Zhidong Teng,et al.  Adaptive synchronization in an array of linearly coupled neural networks with reaction–diffusion terms and time delays , 2012 .

[13]  Lei Guo,et al.  Passivity and Stability Analysis of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions , 2011, IEEE Transactions on Neural Networks.

[14]  Huai-Ning Wu,et al.  Passivity analysis of complex dynamical networks with multiple time-varying delays , 2012 .

[15]  Jinde Cao,et al.  Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller , 2013, SIAM J. Control. Optim..

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

[17]  Junguo Lu.  Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

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

[19]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

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

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

[22]  Jinde Cao,et al.  Passivity of uncertain neural networks with both leakage delay and time-varying delay , 2012 .

[23]  Shouming Zhong,et al.  Improved passivity criteria for memristive neural networks with interval multiple time-varying delays , 2016, Neurocomputing.

[24]  Cao Jinde,et al.  Adaptive pinning synchronization of coupled neural networks with mixed delays and vector-form stochastic perturbations , 2012 .

[25]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

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

[27]  Xin Wang,et al.  Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays , 2014, Neural Networks.

[28]  Hermann Haken.  Pattern Recognition and Synchronization in Pulse-Coupled Neural Networks , 2006 .

[29]  Shouming Zhong,et al.  New passivity criteria for uncertain neural networks with time-varying delay , 2016, Neurocomputing.

[30]  Wu Jigang,et al.  Pinning Control for Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topologies , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[31]  Jun-Guo Lu,et al.  Robust Global Exponential Stability for Interval Reaction–Diffusion Hopfield Neural Networks With Distributed Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  Zengyun Wang,et al.  Synchronization analysis of linearly coupleddelayed neural networks with discontinuous activations , 2015 .

[33]  Huai-Ning Wu,et al.  Pinning Control Strategies for Synchronization of Linearly Coupled Neural Networks With Reaction–Diffusion Terms , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Josep M. Guerrero,et al.  Hybrid Three-Phase/Single-Phase Microgrid Architecture With Power Management Capabilities , 2015, IEEE Transactions on Power Electronics.

[35]  G. L. Santosuosso.  Passivity of nonlinear systems with input-output feedthrough , 1997, Autom..

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

[37]  Jinde Cao,et al.  New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays , 2016, Neurocomputing.

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

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

[40]  Huai-Ning Wu,et al.  Robust stability and robust passivity of parabolic complex networks with parametric uncertainties and time-varying delays , 2012, Neurocomputing.

[41]  Jie Liu,et al.  Multi-focus image fusion based on robust principal component analysis and pulse-coupled neural network , 2014 .

[42]  Hong Qu,et al.  Computing k shortest paths using modified pulse-coupled neural network , 2015, Neurocomputing.

[43]  Josep M. Guerrero,et al.  A Multiagent-Based Consensus Algorithm for Distributed Coordinated Control of Distributed Generators in the Energy Internet , 2015, IEEE Transactions on Smart Grid.