This article inspects the problem of robust synchronization for uncertain Markovian jumping complex interconnected neural networks with randomly occurring uncertainties and time delays. The uncertainties considered here occur randomly and are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. The presence of sensor faults may cause degradation or even instability of the entire network. Therefore, control laws are designed with sensor faults to ensure the controlled synchronization of the complex interconnected neural networks. Three types of fault-tolerant controls are designed based on the Lyapunov stability theory and adaptive schemes which include passive and adaptive fault-tolerant control laws. By constructing a new Lyapunov-Krasovskii functional (LKF) and by using Jensen’s inequality with a free-weighting matrix approach, some new delay-dependent synchronization criteria are obtained in terms of linear matrix inequalities (LMIs). By using the Lyapunov stability theory, the existence condition for the adaptive controller that guarantees the robust mean-square synchronization of complex interconnected neural networks in terms of LMIs are derived. Finally, a numerical example is presented to demonstrate the performance of the developed approach.

本文研究了具有随机发生的不确定性和时间延迟的不确定马尔可夫跳跃复杂互连神经网络的鲁棒同步问题。这里考虑的不确定性是随机发生的，并假设遵循某些相互不相关的伯努利分布的白噪声序列。传感器故障的存在可能会导致整个网络的退化甚至不稳定。因此，控制律设计有传感器故障，以确保复杂互连神经网络的受控同步。基于李雅普诺夫稳定性理论和自适应方案设计了三种类型的容错控制，包括被动和自适应容错控制律。通过构造一个新的Lyapunov-Krasovskii 泛函(LKF) 和利用自由加权矩阵方法的Jensen 不等式，根据线性矩阵不等式(LMI) 获得了一些新的延迟相关同步准则。利用Lyapunov稳定性理论，推导了保证复杂互连神经网络鲁棒均方同步的自适应控制器的存在条件。最后，给出了一个数值例子来证明所开发方法的性能。推导了保证复杂互连神经网络鲁棒均方同步的自适应控制器的存在条件。最后，给出了一个数值例子来证明所开发方法的性能。推导了保证复杂互连神经网络鲁棒均方同步的自适应控制器的存在条件。最后，给出了一个数值例子来证明所开发方法的性能。