Fixed-time synchronization of delayed dynamic networks: Average aperiodic intermittent control interval approach

In this paper, aperiodic intermittent control (AIC) is presented for the fixed-time synchronization of delayed dynamic networks. To overcome the difficulty that the AIC strategy cannot solve the fixed-time synchronization of delayed dynamic networks directly, the concept of anaverage intermittent control interval is proposed. Based on this average concept and by constructing an auxiliary function, a new lemma is given, which is used to study the fixed-time synchronization of dynamic networks. The upper/lower bound restrictions on each control width for AIC input are relaxed using average intermittent control. A novel Lyapunov function is proposed, and flexible criteria are established for finite-time/exponential synchronization of general dynamic networks using the average intermittent control strategy. The relationship between the average control interval and intermittent interval with afixed-time is given. Finally, typical networks are used to show the validity of our AIC approach.