School of Mathematics Science, Liaocheng University, Liaocheng, Shandong, 252000, PR China.
Department of Electrical Engineering, Yeungnam University, Kyongsan, 38541, Republic of Korea.
Neural Netw. 2023 Aug;165:213-227. doi: 10.1016/j.neunet.2023.05.034. Epub 2023 May 27.
In this paper, the stochastic sampled-data exponential synchronization problem for Markovian jump neural networks (MJNNs) with time-varying delays and the reachable set estimation (RSE) problem for MJNNs subjected to external disturbances are investigated. Firstly, assuming that two sampled-data periods satisfy Bernoulli distribution, and introducing two stochastic variables to represent the unknown input delay and the sampled-data period respectively, the mode-dependent two-sided loop-based Lyapunov functional (TSLBLF) is constructed, and the conditions for the mean square exponential stability of the error system are derived. Furthermore, a mode-dependent stochastic sampled-data controller is designed. Secondly, by analyzing the unit-energy bounded disturbance of MJNNs, a sufficient condition is proved that all states of MJNNs are confined to an ellipsoid under zero initial condition. In order to make the target ellipsoid contain the reachable set of the system, a stochastic sampled-data controller with RSE is designed. Eventually, two numerical examples and an analog resistor-capacitor network circuit are provided to show that the textual approach can obtain a larger sampled-data period than the existing approach.
本文研究了时变时滞马尔可夫跳变神经网络（MJNNs）的随机采样数据指数同步问题和受外部干扰的 MJNNs 的可达集估计（RSE）问题。首先，假设两个采样数据周期服从伯努利分布，并引入两个随机变量分别表示未知输入延迟和采样数据周期，构造了基于模式相关的双边环Lyapunov 泛函（TSLBLF），并推导出误差系统均方指数稳定的条件。然后，设计了一个基于模式相关的随机采样控制器。其次，通过分析 MJNNs 的单位能量有界干扰，证明了在零初始条件下，MJNNs 的所有状态都限制在一个椭球内。为了使目标椭球包含系统的可达集，设计了一个具有 RSE 的随机采样控制器。最后，通过两个数值例子和一个模拟电阻-电容网络电路，验证了所提方法可以获得比现有方法更大的采样数据周期。
