Stochastic hybrid multi-links networks with mixed delays: stabilisation analysis via aperiodically adaptive intermittent control

Abstract

ABSTRACTThis paper investigates the problem of the mean square exponential stabilisation for stochastic hybrid multi-links networks with mixed delays (SHMND) via aperiodically adaptive intermittent control. Based on a new differential inequality with mixed delays and Markovian switching, two stability criteria are derived, which weakens the restriction on parameter that determines exponential convergence rate and reduces the conservativeness. The intensity of stochastic perturbations, coupling in multi-links and intermittent control gain have a great influence on these stability criteria. Different from the previous work that studying multi-links systems, we utilise Lyapunov method and the tree-cycle identity in graph theory integrating differential inequality techniques. Furthermore, the main results are applied to the stochastic hybrid multi-links oscillators with mixed delays. Finally, we give a numerical example to illustrate the effectiveness of theoretical results.