Delay-dependent passivity criterion for discrete-time delayed standard neural network model

In this paper, the problem of robust passivity for discrete-time delayed standard neural network model (DDSNNM) with time-varying delays and norm-bounded parameters uncertainties is investigated. The model is the interconnection of a linear dynamic system and a bounded static delayed nonlinear operator. The DDSNNM is applied to analyze the passivity of discrete-time recurrent neural networks and synthesize the state-feedback passive controller for discrete-time nonlinear system modeled by the neural networks. By constructing suitable Lyapunov-Krasovskii functional, the delay-dependent passivity criterion for discrete-time delayed standard neural network model is obtained in terms of linear matrix inequality. Numerical examples are given to illustrate the effectiveness of the proposed methods.

[1]  B. Cui,et al.  Robust passive control for uncertain discrete-time systems with time-varying delays☆ , 2006 .

[2]  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).

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

[4]  Emilia Fridman,et al.  On delay-dependent passivity , 2002, IEEE Trans. Autom. Control..

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

[6]  Xiaoou Li,et al.  Some stability properties of dynamic neural networks , 2001 .

[7]  Vimal Singh,et al.  Novel LMI condition for global robust stability of delayed neural networks , 2007 .

[8]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[9]  T. Liao,et al.  Global asymptotic stability for a class of nonlinear neural networks with multiple delays , 2007 .

[10]  Feng Chunbo,et al.  Output feedback dissipative control for linear discrete-time systems with time-delay , 2005 .

[11]  Tao Li,et al.  Further result on asymptotic stability criterion of neural networks with time-varying delays , 2007, Neurocomputing.

[12]  Wu Min,et al.  Delay-dependent passive control for linear systems with delay , 2005 .

[13]  Guan Xin.  ROBUST PASSIVE CONTROL FOR DISCRETE TIME-DELAY SYSTEMS , 2002 .

[14]  Xuyang Lou,et al.  New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, Neurocomputing.

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

[16]  Qiang Zhang,et al.  Delay-dependent global stability results for delayed Hopfield neural networks , 2007 .

[17]  Meiqin Liu,et al.  Delayed Standard Neural Network Models for Control Systems , 2007, IEEE Transactions on Neural Networks.

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

[19]  Ju H. Park,et al.  Novel delay-dependent robust stability criterion of delayed cellular neural networks , 2007 .

[20]  Zidong Wang,et al.  Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis , 2007 .

[21]  Qiang Zhang,et al.  Delay-dependent global stability condition for delayed Hopfield neural networks , 2007 .

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

[23]  K. Gopalsamy,et al.  Exponential stability of continuous-time and discrete-time cellular neural networks with delays , 2003, Appl. Math. Comput..

[24]  Hailin Liu,et al.  Delay-dependent stability for neural networks with time-varying delay , 2007 .

[25]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[26]  Zhang Guijun.  Delay-dependent robust stability analysis for discrete-time systems with multiple delays , 2006 .

[27]  Wu-Hua Chen,et al.  Global exponential stability for discrete-time neural networks with variable delays , 2006 .

[28]  Zidong Wang,et al.  Robust stability of discrete-time stochastic neural networks with time-varying delays , 2008, Neurocomputing.

[29]  Yun Zou,et al.  Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays , 2008, Neurocomputing.

[30]  Tao Li,et al.  Robust stability for neural networks with time-varying delays and linear fractional uncertainties , 2007, Neurocomputing.

[31]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[32]  AN Yi-chun,et al.  Delay-dependent nonfragile passive control for uncertain discrete-time singular systems , 2007 .

[33]  Meiqin Liu.  Robust H∞ control for uncertain delayed nonlinear systems based on standard neural network models , 2008, Neurocomputing.