Event-based fault-tolerant [formula omitted] synchronization for inertial neural networks via a semi-Markov jump approach

Abstract

In this paper, the synchronization problem of semi-Markov jump neural networks with inertial terms is studied. The semi-Markov jump (s-MJ) process is used to describe the random jump parameters in the system, so Weibull distribution is used to replace the exponential distribution of Markov jump process for the sojourn-time (ST) of each mode in the system. First, a second-order differential system is transformed into a first-order differential system by an appropriate vector substitution. Then, by applying passive fault-tolerant control techniques, the master and slave systems can be synchronized even when the controller fails. In addition, in order to reduce the waste of bandwidth, an event-triggered strategy is designed to determine whether the data needs to be transmitted. Then, by constructing a suitable Lyapunov function and using the characteristics of the cumulative distribution function, the sufficient conditions are established to ensure the stochastic stability of the closed-loop system and meet the specified H∞ performance when the controller fails. Finally, a numerical example and an image processing example are given to verify the effectiveness of the proposed method.