Exponential input-to-state stability of recurrent neural networks with multiple time-varying delays

In this paper, input-to-state stability problems for a class of recurrent neural networks model with multiple time-varying delays are concerned with. By utilizing the Lyapunov–Krasovskii functional method and linear matrix inequalities techniques, some sufficient conditions ensuring the exponential input-to-state stability of delayed network systems are firstly obtained. Two numerical examples and its simulations are given to illustrate the efficiency of the derived results.

[1]  A. Michel,et al.  Exponential stability and trajectory bounds of neural networks under structural variations , 1990, 29th IEEE Conference on Decision and Control.

[2]  Choon Ki Ahn An error passivation approach to filtering for switched neural networks with noise disturbance , 2010, Neural Computing and Applications.

[3]  Kiyotoshi Matsuoka,et al.  Stability conditions for nonlinear continuous neural networks with asymmetric connection weights , 1992, Neural Networks.

[4]  Yiguang Hong,et al.  Stabilization of impulsive hybrid systems using quantized input and output feedback , 2012 .

[5]  Sabri Arik,et al.  Global stability analysis of neural networks with multiple time varying delays , 2005, IEEE Transactions on Automatic Control.

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

[7]  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.

[8]  Choon Ki Ahn,et al.  Some new results on stability of Takagi-Sugeno fuzzy Hopfield neural networks , 2011, Fuzzy Sets Syst..

[9]  Gang Feng,et al.  Delay-Dependent $H_{\infty}$ and Generalized $H_{2}$ Filtering for Delayed Neural Networks , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  David Angeli,et al.  A characterization of integral input-to-state stability , 2000, IEEE Trans. Autom. Control..

[11]  Zhong-Ping Jiang,et al.  Finite-Time Input-to-State Stability and Applications to Finite-Time Control Design , 2010, SIAM J. Control. Optim..

[12]  Wei Feng,et al.  New stability criteria for uncertain neural networks with interval time-varying delays , 2008, Cognitive Neurodynamics.

[13]  Choon Ki Ahn Linear Matrix Inequality Optimization Approach to Exponential Robust Filtering for Switched Hopfield Neural Networks , 2012, J. Optim. Theory Appl..

[14]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

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

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

[17]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[18]  Zhichun Yang,et al.  Input-to-state stability of impulsive hybrid systems with stochastic effects , 2012, 2012 24th Chinese Control and Decision Conference (CCDC).

[19]  C. Ahn Robust stability of recurrent neural networks with ISS learning algorithm , 2011 .

[20]  C. Ahn An ℋ∞ approach to stability analysis of switched Hopfield neural networks with time-delay , 2010 .

[21]  Choon Ki Ahn,et al.  ℒ2–ℒ∞ nonlinear system identification via recurrent neural networks , 2010 .

[22]  Yaonan Wang,et al.  Robust stability analysis of delayed Takagi-Sugeno fuzzy Hopfield neural networks with discontinuous activation functions , 2010, Cognitive Neurodynamics.

[23]  S. Arik Stability analysis of delayed neural networks , 2000 .

[24]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[26]  Eduardo Sontag Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[27]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[28]  Song Zhu,et al.  Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays , 2013, Neural Computing and Applications.

[29]  A. N. Michel,et al.  Exponential stability and trajectory bounds of neural networks under structural variations , 1991 .

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

[31]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[32]  Eduardo Sontag Further facts about input to state stabilization , 1990 .