Finite-Time Stabilization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delay

In this paper, the finite-time stabilization problem for memristive Cohen-Grossberg neural networks with time-varying delay is discussed. By using the novel fixed point theory of set-valued maps, we establish the existence theorem of equilibrium point. In order to realize the finite-time stabilization, two different kinds of discontinuous state feedback controllers whether including time-varying delay are designed. Based on the extended Filippov framework and two different kinds of methods whether using finite-time stability theory, some novel sufficient conditions and the upper bound of the settling time for finite-time stabilization are proposed. Finally, two numerical examples are given to demonstrate the validity of theoretical results.

[1]  Muthukumar Palanisamy,et al.  Finite-time stability analysis for fractional-order Cohen–Grossberg BAM neural networks with time delays , 2016, Neural Computing and Applications.

[2]  Xiaodi Li,et al.  Stability of nonlinear differential systems with state-dependent delayed impulses , 2016, Autom..

[3]  Haipeng Peng,et al.  Finite-time projective synchronization of memristor-based delay fractional-order neural networks , 2017 .

[4]  Haijun Jiang,et al.  Finite-time synchronization of memristor-based Cohen-Grossberg neural networks with time-varying delays , 2016, Neurocomputing.

[5]  Lihong Huang,et al.  Finite-time robust synchronization for discontinuous neural networks with mixed-delays and uncertain external perturbations , 2018, Neurocomputing.

[6]  Jinde Cao,et al.  Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks , 2016, Neural Networks.

[7]  Daniel W. C. Ho,et al.  Finite/Fixed-Time Pinning Synchronization of Complex Networks With Stochastic Disturbances , 2019, IEEE Transactions on Cybernetics.

[8]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[9]  Lihong Huang,et al.  Finite-time synchronization of master-slave neural networks with time-delays and discontinuous activations , 2017 .

[10]  Lixiang Li,et al.  Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks , 2018, Commun. Nonlinear Sci. Numer. Simul..

[11]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[12]  Jinde Cao,et al.  Discontinuous Observers Design for Finite-Time Consensus of Multiagent Systems With External Disturbances , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Li-Hong Huang,et al.  Finite-time synchronization by switching state-feedback control for discontinuous Cohen–Grossberg neural networks with mixed delays , 2018, Int. J. Mach. Learn. Cybern..

[14]  Jinde Cao,et al.  Stability analysis of memristor-based fractional-order neural networks with different memductance functions , 2014, Cognitive Neurodynamics.

[15]  L. Chua.  Memristor-The missing circuit element , 1971 .

[16]  Jinde Cao,et al.  A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks , 2014, Neural Networks.

[17]  Jinde Cao.  New results concerning exponential stability and periodic solutions of delayed cellular neural networks , 2003 .

[18]  Lihong Huang,et al.  Finite-time stabilization control of memristor-based neural networks☆ , 2016 .

[19]  Jun Wang,et al.  Global Exponential Synchronization of Two Memristor-Based Recurrent Neural Networks With Time Delays via Static or Dynamic Coupling , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[20]  Jinde Cao,et al.  Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances , 2017 .

[21]  Jinde Cao,et al.  Exponential stability of complex-valued memristor-based neural networks with time-varying delays , 2017, Appl. Math. Comput..

[22]  Leimin Wang,et al.  Finite-Time Stabilizability and Instabilizability of Delayed Memristive Neural Networks With Nonlinear Discontinuous Controller , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.

[24]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[25]  Shiping Wen,et al.  Event-Based Synchronization Control for Memristive Neural Networks With Time-Varying Delay , 2019, IEEE Transactions on Cybernetics.

[26]  Leon O. Chua,et al.  Memristor Bridge Synapse-Based Neural Network and Its Learning , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Lixiang Li,et al.  Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network , 2016, The European Physical Journal B.

[28]  Lihong Huang,et al.  Periodic synchronization in delayed memristive neural networks based on Filippov systems , 2015, J. Frankl. Inst..

[29]  Guodong Zhang,et al.  Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Pinaki Mazumder,et al.  CMOS and Memristor-Based Neural Network Design for Position Detection , 2012, Proceedings of the IEEE.

[32]  K. D. Cantley,et al.  Hebbian Learning in Spiking Neural Networks With Nanocrystalline Silicon TFTs and Memristive Synapses , 2011, IEEE Transactions on Nanotechnology.

[33]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[34]  Lihong Huang,et al.  Finite-time stabilization control for discontinuous time-delayed networks: New switching design , 2016, Neural Networks.

[35]  Jinde Cao,et al.  Finite-Time Stability Analysis for Markovian Jump Memristive Neural Networks With Partly Unknown Transition Probabilities , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[36]  R. Rakkiyappan,et al.  Stability analysis of memristor-based complex-valued recurrent neural networks with time delays , 2016, Complex..

[37]  Zhenyuan Guo,et al.  Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control , 2016, Neural Networks.

[38]  S. Bhat,et al.  Finite-time stability of homogeneous systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).