Less conservative delay-dependent H∞ control of uncertain neural networks with discrete interval and distributed time-varying delays

This paper deals with the robust H ∞ control problem for a class of uncertain neural networks with discrete interval and distributed time-varying delays. The main purpose of this paper is to estimate robust asymptotic stability of the given neural network with H ∞ performance analysis γ. By constructing novel Lyapunov-Krasovskii functionals with triple integral terms, several new less conservative delay-dependent stability conditions for H ∞ control are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed theoretical results. The method given in this paper shows less conservative results when comparing with some existing methods.

[1]  Jian Sun,et al.  Improved stability criteria for neural networks with time-varying delay , 2009 .

[2]  Xiaoping Liu,et al.  Robust Hinfinity control of Takagi-Sugeno fuzzy systems with state and input time delays , 2009, Fuzzy Sets Syst..

[3]  Lei Guo,et al.  Robust H∞ fuzzy control for uncertain nonlinear Markovian jump systems with time-varying delay , 2013, Fuzzy Sets Syst..

[4]  Xiaodong Liu,et al.  New results on delay-dependent robust stability criteria of uncertain fuzzy systems with state and input delays , 2009, Inf. Sci..

[5]  P. Balasubramaniam,et al.  Robust H∞ control for nonlinear uncertain stochastic T-S fuzzy systems with time delays , 2011, Appl. Math. Lett..

[6]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Dong Yue,et al.  New stability criteria of neural networks with interval time-varying delay: A piecewise delay method , 2009, Appl. Math. Comput..

[8]  M. Ali,et al.  Stability analysis of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time varying delays , 2014 .

[9]  Jian Sun,et al.  New delay-dependent stability criteria for neural networks with time-varying interval delay ✩ , 2010 .

[10]  Jinde Cao,et al.  Stability Analysis of Markovian Jump Stochastic BAM Neural Networks With Impulse Control and Mixed Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[11]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

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

[13]  M. Syed Ali,et al.  Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays , 2015, Neurocomputing.

[14]  M. Syed Ali,et al.  Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays , 2015, Neurocomputing.

[15]  Shouming Zhong,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delay , 2011, Appl. Math. Comput..

[16]  M. Ali,et al.  Improved delay-dependent robust H∞ control of an uncertain stochastic system with interval time-varying and distributed delays , 2014 .

[17]  Xiaodi Li,et al.  Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks , 2012, Fuzzy Sets Syst..

[18]  Tingwen Huang,et al.  Brief Papers Further Result on Guaranteed H∞ Performance State Estimation of Delayed Static Neural Networks , 2015 .

[19]  M. Syed Ali,et al.  Robust stability analysis of Takagi—Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays , 2011 .

[20]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks with Time Varying Delays , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[21]  M. Syed Ali,et al.  Novel delay-dependent robust H∞ control of uncertain systems with distributed time-varying delays , 2014, Appl. Math. Comput..

[22]  Pagavathigounder Balasubramaniam,et al.  Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delays , 2014, International Journal of Machine Learning and Cybernetics.

[23]  M. Syed Ali,et al.  Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays , 2014 .

[24]  Xiaofeng Liao,et al.  Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays , 2012, Cognitive Neurodynamics.

[25]  Henryk Górecki,et al.  Analysis and Synthesis of Time Delay Systems , 1989 .

[26]  Ju H. Park,et al.  New and improved results on stability of static neural networks with interval time-varying delays , 2014, Appl. Math. Comput..

[27]  Xiangjun Xie,et al.  New asymptotic stability criteria for neural networks with time-varying delay , 2010 .

[28]  Ju H. Park,et al.  On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov-Krasovskii functional , 2014, Commun. Nonlinear Sci. Numer. Simul..

[29]  Ju H. Park,et al.  New approach to stability criteria for generalized neural networks with interval time-varying delays , 2015, Neurocomputing.

[30]  Changyin Sun,et al.  Improved delay-dependent stability criteria for neural networks with time-varying delay , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[31]  M. Syed Ali,et al.  Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays , 2011, Math. Comput. Model..

[32]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

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

[34]  Qing-Long Han,et al.  A New $H_{{\bm \infty}}$ Stabilization Criterion for Networked Control Systems , 2008, IEEE Transactions on Automatic Control.

[35]  Ju H. Park,et al.  A study on H∞ state estimation of static neural networks with time-varying delays , 2014, Appl. Math. Comput..

[36]  J. Qiu,et al.  New robust stability criteria for uncertain neural networks with interval time-varying delays , 2009 .

[37]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[38]  Dong Yue,et al.  Delay-dependent robust Hinfinity control for T-S fuzzy system with interval time-varying delay , 2009, Fuzzy Sets Syst..

[39]  Hongye Su,et al.  H∞ state estimation of static neural networks with time-varying delay , 2012, Neurocomputing.

[40]  Jinde Cao,et al.  Synchronization Error Estimation and Controller Design for Delayed Lur'e Systems With Parameter Mismatches , 2012, IEEE Transactions on Neural Networks and Learning Systems.