Global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.