Finite-time synchronization of coupled Markovian discontinuous neural networks with mixed delays
Finite-time synchronization of coupled Markovian discontinuous neural networks with mixed delays
复制标题
混合时滞耦合马尔可夫不连续神经网络的有限时间同步
DOI：
10.1007/s00034-016-0408-2
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Jianwen Feng
中科院分区：
文献类型：
--
作者：
杨鑫松;Jinde Cao;Qiang Song;Chen Xu;Jianwen Feng
在Filippov解的框架下，研究了一组具有不连续激活函数、马尔可夫跳跃参数以及离散和无限时间分布时滞(混合时滞)的耦合神经网络的有限时间同步问题。基于新的Lyapunov-Krasovskii泛函和分析技术以及M-矩阵方法，克服了Filippov解的不确定性、时滞以及马尔可夫链带来的困难。得到了保证有限时间内同步的几个充分条件。与已有的关于非时滞系统有限时间同步的结果不同，时滞系统的建立时间不仅依赖于零时误差状态的值，而且还依赖于误差状态的历史、时滞和马尔可夫链的初值。此外，还考虑了具有不同不确定性扰动的耦合神经网络的有限时间同步问题。所得结果也适用于连续非线性系统，本质上推广了现有的只能有限时间同步或镇定非时滞系统的结果。最后给出了数值算例，验证了理论结果的有效性。
This paper is concerned with finite-time synchronization in an array of coupled neural networks with discontinuous activation functions, Markovian jumping parameters, as well as discrete and infinite-time distributed delays (mixed delays) under the framework of Filippov solution. Based on novel Lyapunov–Krasovskii functionals and analytical techniques andM-matrix method, the difficulties caused by the uncertainties of Filippov solutions, time delays, as well as Markov chain are overcome. Several sufficient conditions are obtained to guarantee the synchronization in finite time. Different from existing results on finite-time synchronization of non-delayed systems, the settling time for time-delay systems is dependent not only on the values of the error state at time zero, but also on the histories of the error state, the time delays, and the initial value of Markov chain. Moreover, finite-time synchronization of the coupled neural networks with nonidentical uncertain perturbations is also considered. The obtained results are also applicable to continuous nonlinear systems, which essentially extend existing results which can only finite-timely synchronize or stabilize non-delayed systems. Finally, numerical examples are given demonstrate the effectiveness of the theoretical results.