异步跳变惯性神经网络的有限时间同步

Finite-time Synchronization of Asynchronous Jump Inertial Neural Networks

针对一类由时滞惯性神经网络组成的马尔可夫异步跳变驱动-响应系统,研究了其在有限时间区间上的同步问题。首先,为了解决推导同步准则过程中的困难,设计了一个非连续的针对闭环系统的控制器;然后,基于李雅普诺夫理论,提出了一些新的李雅普诺夫泛函,并结合反凸组合方法和自由权矩阵方法,对李雅普诺夫泛函的导数进行了合理且有效地放缩;最后,根据所设李雅普诺夫泛函的特征以及系统初始条件,给出了一个较小保守性的有限时间同步结果。数值仿真和保密通信应用实例仿真说明了该控制器设计方法的有效性和实用性。

For a class of asynchronous Markov jumping drive-response systems composed of time-delay inertial neural networks, the issue of synchronization within a finite-time interval is investigated. Firstly, in order to solve the difficulty in deriving the synchronization criterion, a non-continuous controller for closed-loop systems is designed. Then, based on Lyapunov theory, some new Lyapunov functionals are proposed, and by combining with the reciprocally convex combination approach and the free-weighting matrix method, the derivatives of Lyapunov functionals can be reasonably and effectively scaled. Finally, according to the characteristics of the proposed Lyapunov functionals and the initial conditions of the system, a less conservative finite-time synchronization criterion is given. The effectiveness and practicability of the proposed controller design method is illustrated by a numerical simulation and a secure communication application example.