Abstract
Aiming at the problem of fixed and preassigned-time synchronization of drive-response networks with discontinuous activation function, we derive a fixed-time stability theorem with more accurate stable time estimation for discontinuous systems by comparison principle and variable substitution. We design a fixed-time synchronization controller without linear term and a preassigned-time synchronization controller with limited control gain. Based on the proposed theorem and controller, together with the theory of discontinuous differential equations, we obtain the sufficient conditions for realizing fixed-time synchronization of drive-response networks with discontinuous activation function, and the sufficient condition for realizing the preassigned-time synchronization of drive-response networks with discontinuous activation function. Wherein, the synchronization time can be prespecified according to the actual situation, and it is independent of the initial value of the system and the controller parameters. The numerical simulation results verify the correctness of the stability theorem and the accuracy of the synchronization time estimation.
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