Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties

This paper investigates the problem of robust dissipativity analysis for uncertain neural networks with time-varying delay. The norm-bounded uncertainties enter into the neural networks in randomly ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. By employing the linear matrix inequality (LMI) approach, a sufficient condition is established to ensure the robust stochastic stability and dissipativity of the considered neural networks. Some special cases are also considered. Two numerical examples are given to demonstrate the validness and the less conservatism of the obtained results.

[1]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[2]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[3]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[4]  Madan M. Gupta,et al.  Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory , 2003 .

[5]  S. Arik.  On the global dissipativity of dynamical neural networks with time delays , 2004 .

[6]  Q. Song,et al.  Global dissipativity of neural networks with both variable and unbounded delays , 2005 .

[7]  Shengyuan Xu,et al.  Improved global robust asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[9]  Izumi Masubuchi,et al.  Dissipativity inequalities for continuous-time descriptor systems with applications to synthesis of control gains , 2006, Syst. Control. Lett..

[10]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[11]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[12]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[13]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

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

[15]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[16]  James Lam,et al.  A New Criterion of Delay-Dependent Asymptotic Stability for Hopfield Neural Networks With Time Delay , 2008, IEEE Transactions on Neural Networks.

[17]  Huijun Gao,et al.  Stabilization of Networked Control Systems With a New Delay Characterization , 2008, IEEE Transactions on Automatic Control.

[18]  Gang Feng,et al.  Reliable dissipative control for stochastic impulsive systems , 2008, Autom..

[19]  James Lam,et al.  Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays , 2008, Int. J. Control.

[20]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

[21]  Jinde Cao,et al.  Global dissipativity of stochastic neural networks with time delay , 2009, J. Frankl. Inst..

[22]  Ju H. Park,et al.  Further results on state estimation for neural networks of neutral-type with time-varying delay , 2009, Appl. Math. Comput..

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

[24]  Ju H. Park,et al.  Synchronization Criterion for Lur’e Systems via Delayed PD Controller , 2010, J. Optim. Theory Appl..

[25]  R. Lu,et al.  Passivity analysis of stochastic time-delay neural networks , 2010 .

[26]  Kai Zhang,et al.  Exponential stability for switched Cohen–Grossberg neural networks with average dwell time , 2011, Proceedings of the 29th Chinese Control Conference.

[27]  Wei Xing Zheng,et al.  Exponential Stability Analysis for Delayed Neural Networks With Switching Parameters: Average Dwell Time Approach , 2010, IEEE Transactions on Neural Networks.

[28]  Ju H. Park,et al.  Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays , 2010 .

[29]  Ju H. Park,et al.  Dissipativity analysis for singular systems with time-varying delays , 2011, Appl. Math. Comput..

[30]  Yong He,et al.  Passivity analysis for neural networks with a time-varying delay , 2011, Neurocomputing.

[31]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems with Mixed Time-delays , Randomly Occurring Uncertainties and Nonlinearities , 2011 .

[32]  James Lam,et al.  α-Dissipativity analysis of singular time-delay systems , 2011, Autom..

[33]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[34]  Zidong Wang,et al.  A Stochastic Sampled-Data Approach to Distributed $H_{\infty }$ Filtering in Sensor Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  James Lam,et al.  Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[36]  Sabri Arik,et al.  Further analysis of global robust stability of neural networks with multiple time delays , 2012, J. Frankl. Inst..

[37]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

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

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