Finite-Time Synchronization of Coupled Markovian Discontinuous Neural Networks with Mixed Delays

Abstract

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 and M-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.