Fixed-time synchronization of large-scale systems via aperiodically intermittent control

This paper studies the fixed-time synchronization of large-scale systems. An aperiodically intermittent control (AIC) based on the average control rate is introduced to achieve fixed-time synchronization for the first time. Compared with previous work, the AIC based on the average control rate reduces the limitation of control width and rest width, thus, the conservativeness is reduced. Moreover, the designed control uses the hyperbolic sine function instead of the sign function, which can avoid the chattering phenomena. A concession is made between rest and control intervals by constructing the auxiliary timers, such that the derivative of Lyapunov function (ignoring the exogenous disturbance) built is always non-positive. Then by combining the graph theory and Lyapunov method, some sufficient conditions are given. Finally, a numerical example is presented to verify the effectiveness of the results developed.