Pinning synchronization for delayed coupling complex dynamical networks with incomplete transition rates Markovian jump

Abstract

In this paper, the synchronization problem is investigated for a class of time-varying delayed coupling complex dynamical networks subject to incomplete transition rates Markovian switching typologies via pinning control scheme. Compared with most of previous relative networks, a more general network model is discussed and in which the transition rates in Markovian processes are uncertain or completely unknown. The complete knowledge on the transition rates is difficult to precisely acquire on account of the limitations of equipment and environmental impacts. Only a single feedback controller is utilized and, by constructing time dependent Lyapunov–Krasovskii functions, applying an extended Jensen’s integral inequality as well as some inequality techniques, some criteria are obtained for guaranteeing stochastic synchronization of considered networks. Moreover, similar results can be also presented for Markovian jump complex dynamical networks without time-varying delay. The obtained results improve and extend some existing relevant results. In the end, some simulation examples are provided to illustrate the effectiveness of the proposed method.