Novel adaptive synchronization in finite-time and fixed-time for impulsive complex networks with semi-Markovian switching

This paper intensively studied the finite-time (FNT) and fixed-time (FXT) synchronization issues for complex networks (CNs) with semi-Markovian switching and impulsive effect. The impulses are assumed to be independent of the semi-Markovian switching. Firstly, a unified FNT and FXT stability criterion of impulsive dynamical system with time-varying delays is extended by comparison principle. Secondly, two novel hybrid control schemes, which are composed of adaptive gain and switching state-feedback are proposed. Thirdly, by employing Kronecker product, Lyapunov-Krasovskii functional and inequality technique, FNT and FXT synchronization criteria for impulsive CNs with semi-Markovian switching are presented in a set of low-dimensional linear matrix inequalities, and the settling times are computed respectively. Finally, simulations are given to verify the proposed adaptive FNT and FXT synchronization criteria. •A unified finite/fixed-time stability criterion of impulsive system is extended.•The impulsive effect and semi-Markovian switching are considered in complex networks.•Under two hybrid controllers, the finite/fixed-time synchronization criteria are established.•The finite/fixed-time synchronization settling times are given by some concrete expressions.