Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay

This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results.

[1]  H. B. Huang,et al.  Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty , 2005 .

[2]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[3]  Jinde Cao,et al.  Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Jinde Cao,et al.  Passivity analysis for switched generalized neural networks with time-varying delay and uncertain output , 2013, IMA J. Math. Control. Inf..

[5]  Yang Tang,et al.  Stability analysis of switched stochastic neural networks with time-varying delays , 2014, Neural Networks.

[6]  Hamid Reza Karimi,et al.  Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps , 2014, Neurocomputing.

[7]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[8]  Yuqiang Wu,et al.  Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay ☆ , 2011 .

[9]  Quanxin Zhu,et al.  Synchronization of switched neural networks with mixed delays via impulsive control , 2011 .

[10]  Zidong Wang,et al.  Asymptotic stability for neural networks with mixed time-delays: The discrete-time case , 2009, Neural Networks.

[11]  Rathinasamy Sakthivel,et al.  Linear matrix inequality approach to stochastic stability of uncertain delayed BAM neural networks , 2013 .

[12]  Shihua Li,et al.  Finite-time boundedness and stabilization of switched linear systems , 2010, Kybernetika.

[13]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[14]  Fei Liu,et al.  Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters , 2013, Neurocomputing.

[15]  Youxian Sun,et al.  Absolute Exponential Stability of Recurrent Neural Networks With Generalized Activation Function , 2008, IEEE Transactions on Neural Networks.

[16]  Rathinasamy Sakthivel,et al.  Design of state estimator for bidirectional associative memory neural networks with leakage delays , 2015, Inf. Sci..

[17]  A. Arunkumar,et al.  Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks. , 2014, ISA transactions.

[18]  Ying-Xu Yang,et al.  Finite‐time stability of switched positive linear systems , 2014 .

[19]  Shengyuan Xu,et al.  Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Jinde Cao,et al.  Synchronization control of switched linearly coupled neural networks with delay , 2010, Neurocomputing.

[21]  Zidong Wang,et al.  Exponential stability of uncertain stochastic neural networks with mixed time-delays , 2007 .

[22]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[23]  Zhengzhi Han,et al.  Robust finite-time stability and stabilisation of switched positive systems , 2014 .

[24]  Zhongyang Fei,et al.  Finite-time H∞ control of switched systems with mode-dependent average dwell time , 2014, J. Frankl. Inst..

[25]  Jinde Cao,et al.  Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure , 2007 .

[26]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[27]  Yanjun Shen,et al.  LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties , 2008, Neurocomputing.

[28]  Rathinasamy Sakthivel,et al.  Robust reliable H∞ control for stochastic neural networks with randomly occurring delays , 2015, Neurocomputing.

[29]  Mohamad H. Hassoun,et al.  Recurrent neural nets as dynamical Boolean systems with application to associative memory , 1997, IEEE Trans. Neural Networks.

[30]  Rathinasamy Sakthivel,et al.  Robust stability criteria for discrete-time switched neural networks with various activation functions , 2012, Appl. Math. Comput..

[31]  Hao Liu,et al.  Finite-time stabilization and boundedness of switched linear system under state-dependent switching , 2013, J. Frankl. Inst..

[32]  Jun Cheng,et al.  Finite-time boundedness of state estimation for neural networks with time-varying delays , 2014, Neurocomputing.

[33]  P. OrŁowski.  Methods for stability evaluation for linear time varying, discrete-time systems on finite time horizon , 2006 .

[34]  Zhengqiu Zhang,et al.  Novel LMI-based condition on global asymptotic stability for BAM neural networks with reaction-diffusion terms and distributed delays , 2014, Neurocomputing.