Finite-Time Control of Fuzzy Competitive Networks via Comparison Method and Bounded Control

This article aims to consider the finite-time synchronization of a class of discontinuous fuzzy competitive networks with nondifferential leakage delays. Different from the previous competitive networks and leakage-delayed networks, the activation functions are discontinuous and the leakage delays are nondifferential. Without using the Lyapunov function methods, the synchronization in a finite time is investigated based on the comparison principle and inequality techniques, which are used for the first time in the study of the competitive networks and leakage-delayed networks. Moreover, the feedback controller and bounded feedback controller are designed to help achieve the finite-time synchronization. The bounded feedback controller is formulated by the function
$\arctan$
and a new inequality lemma is given, which plays a vital role in achieving the synchronization via bounded feedback controller. Although both controllers can help achieve the finite-time synchronization, it can be found that there is a big difference that the value of feedback controller is greatly influenced by system's state variables, but bounded controller is not. Such fact leads to different settling-times. The conclusion is that bounded controller has more advantages in shortening convergence time through numerical simulations.