具有连续分布时变时滞神经网络时滞相关稳定性判据
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摘要
为研究具有连续分布时变时滞神经网络的全局稳定性条件,利用增广型Lyapunov-Krasovskii泛函(LKF)和运用多种积分不等式缩放技巧,推导了两种保守性相对较小的时滞相关稳定性判据.为进一步降低稳定性判据的保守性,通过改进增广型LKF,结合神经元激活函数的约束条件,得到了基于线性矩阵不等式形式的神经网络时滞相关渐近稳定性条件.结果表明,新的LKF方法具有更好的效果,且稳定性判据的运算负担更低,算例证实了该方法的有效性.
This paper investigates the delay-dependent stability for continuous neural networks with time-varying delay. Two novel and less conservative stability criteria are derived by employing Lyapunov-Krasovskii functional(LKF) and several suitable integral inequalities. An augmented LKF which considers more information of the slope of neuron activation functions is developed for further reducing the conservatism of stability criteria. Moreover, it is found that the introduced LKF approach leads to better results and the derived stability criteria have lower computational burden. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
This paper investigates the delay-dependent stability for continuous neural networks with time-varying delay. Two novel and less conservative stability criteria are derived by employing Lyapunov-Krasovskii functional(LKF) and several suitable integral inequalities. An augmented LKF which considers more information of the slope of neuron activation functions is developed for further reducing the conservatism of stability criteria. Moreover, it is found that the introduced LKF approach leads to better results and the derived stability criteria have lower computational burden. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
引文
[1] KWON O M, PARK M J, LEE S M, et al. Stability for neural networks with time-varying delays via some new approaches [J]. IEEE Trans Neural Netw Learn Syst, 2013, 24(2): 181-193.
[2] CHEN Yun, ZHENG Weixing. Stability analysis of time-delay neural networks subject to stochastic perturbations [J]. IEEE Trans Cybern, 2013, 43(6): 2122-2134.
[3] ZHANG Chuanke, HE Yong, JIANG Lin, et al. Delay-dependent stability criteria for generalized neural networks with two delay components [J]. IEEE Trans Neural Netw Learn Syst, 2014, 25(7): 1263-1276.
[4] GE Chao, HUA Changchun, GUAN Xinping. New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach [J]. IEEE Trans Neural Netw Learn Syst, 2014, 25(7): 1378-1383.
[5] ZHANG Huaguang, WANG Zhanshan, LIU Derong. A comprehensive review of stability analysis of continuous-time recurrent neural networks [J]. IEEE Trans Neural Netw Learn Syst, 2014, 25(7): 1229-1262.
[6] WANG Zhanshan, LIU Lei, SHAN Qihe, et al. Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method [J]. IEEE Trans Neural Netw Learn Syst, 2015, 26(10): 2589-2595.
[7] CHEN Wuhua, ZHENG Weixing. Robust stability analysis for stochastic neural networks with time-varying delay [J]. IEEE Trans Neural Networks, 2010, 21(3): 508-514.
[8] ZHENG Chengde, ZHANG Huaguang, WANG Zhanshan. Improved robust stability criteria for delayed cellular neural networks via the LMI approach [J]. IEEE Trans Circuit Syst-II, 2010, 57(1): 41-45.
[9] LI Tao, YE Xiaoling. Improved stability criteria of neural networks with time-varying delays: an augmented LKF approach [J]. Neurocomputing, 2010, 73(1): 1038-1047.
[10] STOJANOVIC S B. Further improvement in delay-dependent finite-time stability criteria for uncertain continuous-time systems with time-varying delays [J]. IET Control Theory Appl, 2016, 10(8): 926-938.
[11] TIAN Junkang, ZHONG Shouming. Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components [J]. Neurocomputing, 2012, 77(1): 114-119.
[12] MANIVANNAN R, SAMIDURAI R, CAO J D, et al. Stability analysis of interval time-varying delayed neural networks including neutral time-delay and leakage delay [J]. Chaos Soliton Fractal, 2018, 114: 433-445.
[13] ZENG Hongbing, HE Yong, WU Min, et al. Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays [J]. Neural Network, 2011, 22(5): 806-812.
[2] CHEN Yun, ZHENG Weixing. Stability analysis of time-delay neural networks subject to stochastic perturbations [J]. IEEE Trans Cybern, 2013, 43(6): 2122-2134.
[3] ZHANG Chuanke, HE Yong, JIANG Lin, et al. Delay-dependent stability criteria for generalized neural networks with two delay components [J]. IEEE Trans Neural Netw Learn Syst, 2014, 25(7): 1263-1276.
[4] GE Chao, HUA Changchun, GUAN Xinping. New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach [J]. IEEE Trans Neural Netw Learn Syst, 2014, 25(7): 1378-1383.
[5] ZHANG Huaguang, WANG Zhanshan, LIU Derong. A comprehensive review of stability analysis of continuous-time recurrent neural networks [J]. IEEE Trans Neural Netw Learn Syst, 2014, 25(7): 1229-1262.
[6] WANG Zhanshan, LIU Lei, SHAN Qihe, et al. Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method [J]. IEEE Trans Neural Netw Learn Syst, 2015, 26(10): 2589-2595.
[7] CHEN Wuhua, ZHENG Weixing. Robust stability analysis for stochastic neural networks with time-varying delay [J]. IEEE Trans Neural Networks, 2010, 21(3): 508-514.
[8] ZHENG Chengde, ZHANG Huaguang, WANG Zhanshan. Improved robust stability criteria for delayed cellular neural networks via the LMI approach [J]. IEEE Trans Circuit Syst-II, 2010, 57(1): 41-45.
[9] LI Tao, YE Xiaoling. Improved stability criteria of neural networks with time-varying delays: an augmented LKF approach [J]. Neurocomputing, 2010, 73(1): 1038-1047.
[10] STOJANOVIC S B. Further improvement in delay-dependent finite-time stability criteria for uncertain continuous-time systems with time-varying delays [J]. IET Control Theory Appl, 2016, 10(8): 926-938.
[11] TIAN Junkang, ZHONG Shouming. Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components [J]. Neurocomputing, 2012, 77(1): 114-119.
[12] MANIVANNAN R, SAMIDURAI R, CAO J D, et al. Stability analysis of interval time-varying delayed neural networks including neutral time-delay and leakage delay [J]. Chaos Soliton Fractal, 2018, 114: 433-445.
[13] ZENG Hongbing, HE Yong, WU Min, et al. Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays [J]. Neural Network, 2011, 22(5): 806-812.