Event-Based Pinning Synchronization Control for Time-Delayed Complex Dynamical Networks: The Finite-Time Boundedness

The paper is concerned with the synchronization control issue for a kind of nonlinear discrete time-delayed complex dynamical networks. To improve energy efficiency, a dynamic event-triggering strategy is introduced to regulate the signal transmission from the controller to the actuator. Then, the event-based pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in control process. Subsequently, a new concept of finite-time boundedness in the mean square is put forward to evaluate the synchronization control performance by means of a settling-like time function. Furthermore, by using the Lyapunov stability theory and the stochastic analysis technique, a sufficient condition is provided to ensure that the synchronization error is finite-time bounded in the mean square with a prescribed error upper bound in the presence of both time-delay and external noise disturbances. By solving an optimization problem with some inequality constraints, the desired controller gain matrix is parameterized to minimize the settling-like time. Finally, a numerical simulation example is carried out to illustrate the effectiveness and usefulness of the obtained theoretical results.