Synchronization of Delayed Complex Networks on Time Scales via Aperiodically Intermittent Control Using Matrix-Based Convex Combination Method

This article reconsiders synchronization problem of linear complex networks with time-varying delay on time scales. For different types of time scales, aperiodically intermittent control scheme is established by using a matrix-based convex combination method, which has great potential in reducing control consumption and saving communication bandwidth. By employing a common Lyapunov function, aperiodically intermittent controllers are utilized successfully to achieve synchronization of linear delayed complex networks on special time scales onto an isolated node. Next, by constructing a special Lyapunov function with time-varying coefficients, sufficient criteria that consist of two linear matrix inequalities are demonstrated to make linear delayed complex networks on general time scales synchronized onto an isolated system with an exponential convergence rate given in advance. Due to delayed complex networks in this article defined on time scales, the proposed control schemes are applicable to continuous-time networks, their discrete-time forms, and any combination of them. Four numerical examples are offered to highlight the effectiveness and superiority of the proposed aperiodically intermittent control schemes at last.

Automated summary

This article reconsidered the synchronization problem of linear complex networks with time-varying delay on time scales and proposed aperiodically intermittent control schemes for different types of time scales. By using a common Lyapunov function and a special Lyapunov function with time-varying coefficients, synchronization of linear delayed complex networks onto an isolated node was successfully achieved on special and general time scales.