Delay Event-Triggered Control for Stability Analysis of Complex Networks

This brief is concerned with exponential stability of delayed complex networks. Different from existing literature, an extended control is proposed, namely delay event-triggered control, in which the update of control signals is determined by the event-triggered mechanism. Both continuous event-triggered mechanism and periodic event-triggered mechanism are developed by continuous measuring and periodic sampling, respectively. The continuous event-triggered mechanism with waiting time is proposed to ensure that the existence of the minimum inter-execution time has a positive minimum value. The upper bound of the sampling period is given for the periodic event-triggered mechanism and an estimation about sampling/execution error is obtained to assess the network states. Subsequently, by employing the Lyapunov method and graph-theoretic approach, stability criteria for delayed complex networks under delay event-triggered control are established. Ultimately, the analytical results are applied into single-link robot arm systems and a corresponding numerical example is given to illustrate the effectiveness and feasibility of theoretical claims.