Exponential synchronization of complex dynamical network with mixed time-varying and hybrid coupling delays via intermittent control

In this paper, we shall investigate the problem of exponential synchronization for complex dynamical network with mixed time-varying and hybrid coupling delays, which is composed of state coupling, interval time-varying delay coupling and distributed time-varying delay coupling. The designed controller ensures that the synchronization of delayed complex dynamical network are proposed via either feedback control or intermittent feedback control. The constraint on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. We use common unitary matrices, and the problem of synchronization is transformed into the stability analysis of some linear time-varying delay systems. This is based on the construction of an improved Lyapunov-Krasovskii functional combined with the Leibniz-Newton formula and the technique of dealing with some integral terms. New synchronization criteria are derived in terms of LMIs which can be solved efficiently by standard convex optimization algorithms. Two numerical examples are included to show the effectiveness of the proposed feedback control and intermittent feedback control scheme.