Improved fixed-time stability results and application to synchronization of discontinuous neural networks with state-dependent switching

In this article, we considered the fixed-time stability (FXT) of a type of discontinuous dynamical system. First, we introduced some new FXT stability results via variable substitutions and using inequality techniques, which are more accurately estimate the upper bound of settling time (ST). Then, based on the established results and using the differential inclusion theory, we investigated the FXT synchronization of a type of general neural networks (NNs) with state-dependent switching coefficients and discontinuous neuron activation functions via introducing a type of discontinuous controller which is more simple compared to existing results. In addition, the estimated upper bound of ST shown to be independent to the initial values of considered drive-response networks, and it is much smaller and nearer to the real synchronization time than those given in the previously published works. Lastly, two numerical examples are given to demonstrate the feasibility of our derived theoretical results. We believe that the results of this article can give some new insights for the FXT stabilization and FXT synchronization analysis of state-dependent switching dynamics with or without discontinuous right-hand sides.