Lag synchronization analysis of semi-Markovian jumping CVNs with time-varying delay: Mode-dependent distributed delayed control scheme

Abstract

This paper is devoted to addressing the lag synchronization issue of semi-Markovian jumping complex-valued networks with time-varying delay. Firstly, two types of mode-dependent controllers are designed, i.e., a continuous distributed delayed memorized controller and a discrete distributed delayed impulsive controller, which are utilized to facilitate lag synchronization between the considered master and slave systems. Secondly, by introducing some novel integral inequalities, the achieved results not only effectively overcome the limitation $\dot{d}\left(t\right)<1$ in earlier literature, but also expand the feasible domain because of the addition of relaxed matrices $N$ and $X$. Additionally, sufficient conditions for attaining mean-square lag synchronization of the master–slave systems can be obtained by resorting to numerous inequality approaches, stochastic analysis techniques, and Lyapunov stability theory. Meanwhile, the desired controller gain matrices can be designed by solving derived matrix inequalities. As a final point, two numerical examples are proposed to validate the established theoretical criteria.