Synchronization of stochastic hybrid coupled systems with multi-weights and mixed delays via aperiodically adaptive intermittent control

Abstract

In this paper, synchronization problem of stochastic hybrid coupled systems with multi-weights and mixed delays (SHSMD) is researched via aperiodically adaptive intermittent control, and both multi-weights and mixed delays are taken into account. In order to extend the existing Halanay-type differential inequalities to systems with mixed delay and Markovian jump, two novel differential inequalities are established, based on which the exponential synchronization of SHSMD is analyzed. In virtue of differential inequality technique, graph theory and Lyapunov method, several synchronization criteria are obtained. Because of using the established differential inequalities, the conditions on the delay-related parameters affecting the exponential convergence rate are weakened, which results in the exponential synchronization criteria obtained in this paper being less conservative than those in the existing literature. To illustrate the effectiveness of the stated theoretical results, an application to Chua’s circuits network is provided and a numerical example is also given finally.