Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions

Without assuming the boundedness and monotonicity of neuron activations, we investigate passivity of delayed neural networks with discontinuous activations. Based on differential inclusion theory, sufficient conditions are established in form of linear matrix inequality by employing the generalized Lyapunov approach. In addition, a kind of control input is designed to stabilize neural network with activation functions having special form. Finally, some numerical examples are proposed to show the effectiveness of developed results.

[1]  Jinde Cao,et al.  Stability of Markovian jump neural networks with impulse control and time varying delays , 2012 .

[2]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[3]  Song Zhu,et al.  Passivity analysis of stochastic delayed neural networks with Markovian switching , 2011, Neurocomputing.

[4]  Lihong Huang,et al.  On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions , 2012, Neural Networks.

[5]  Ju H. Park,et al.  Passivity-based control for Hopfield neural networks using convex representation , 2011, Appl. Math. Comput..

[6]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[7]  C. Ahn.  Switched exponential state estimation of neural networks based on passivity theory , 2012 .

[8]  Ju H. Park,et al.  Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates , 2012 .

[9]  Tianping Chen,et al.  Complete stability of cellular neural networks with unbounded time-varying delays , 2012, Neural Networks.

[10]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[11]  Z. Zeng,et al.  Global exponential stability in Lagrange sense for recurrent neural networks with time delays , 2008 .

[12]  Eva Kaslik,et al.  Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis , 2011, Neural Networks.

[13]  Jun Wang,et al.  Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching , 2009, IEEE Transactions on Neural Networks.

[14]  Jun Wang,et al.  A general projection neural network for solving monotone variational inequalities and related optimization problems , 2004, IEEE Transactions on Neural Networks.

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

[16]  Lihong Huang,et al.  Global asymptotic stability of neural networks with discontinuous activations , 2009, Neural Networks.

[17]  James Lam,et al.  Stability analysis of static recurrent neural networks using delay-partitioning and projection , 2009, Neural Networks.

[18]  Song Zhu,et al.  Exponential passivity of neural networks with time-varying delay and uncertainty , 2010 .

[19]  Huaguang Zhang,et al.  Novel Stability Analysis for Recurrent Neural Networks With Multiple Delays via Line Integral-Type L-K Functional , 2010, IEEE Transactions on Neural Networks.

[20]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[21]  Zengyun Wang,et al.  Robust Stability Criterion for Delayed Neural Networks with Discontinuous Activation Functions , 2009, Neural Processing Letters.

[22]  Huaguang Zhang,et al.  Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays , 2009, Neurocomputing.

[23]  Jinde Cao,et al.  A feedback neural network for solving convex constraint optimization problems , 2008, Appl. Math. Comput..

[24]  Tianping Chen,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions , 2005, Neural Networks.

[25]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Walter Allegretto,et al.  Common Asymptotic Behavior of Solutions and Almost Periodicity for Discontinuous, Delayed, and Impulsive Neural Networks , 2010, IEEE Transactions on Neural Networks.

[27]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Sabri Arik,et al.  Equilibrium and stability analysis of delayed neural networks under parameter uncertainties , 2012, Appl. Math. Comput..

[29]  Sitian Qin,et al.  Global Exponential Stability and Global Convergence in Finite Time of Neural Networks with Discontinuous Activations , 2009, Neural Processing Letters.

[30]  Choon Ki Ahn,et al.  Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay , 2010, Inf. Sci..

[31]  Jinde Cao,et al.  Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions , 2012, Int. J. Syst. Sci..

[32]  Zhigang Zeng,et al.  Exponential Stabilization of Memristive Neural Networks With Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[33]  Yang Tang,et al.  Stability of delayed neural networks with time-varying impulses , 2012, Neural Networks.

[34]  Ju H. Park,et al.  A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays , 2011, Appl. Math. Comput..

[35]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[36]  Xiaoou Li,et al.  Passivity Analysis of Dynamic Neural Networks with Different Time-scales , 2006, Neural Processing Letters.

[37]  Naira Hovakimyan,et al.  Passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems , 2005, IEEE Transactions on Neural Networks.

[38]  Tianping Chen,et al.  Almost Periodic Dynamics of a Class of Delayed Neural Networks with Discontinuous Activations , 2008, Neural Computation.