Finite-time/fixed-time stability and stabilization of a class of delayed neural networks system with discontinuous activation

This paper focuses to analyze the finite-time stability (FNTS) and fixed-time stability (FXTS) of a class of discontinuous neural networks (NNs) with time-varying delays. Firstly, considering the fuzzy logics and discontinuities in the NNs, a novel FNTS/FXTS approach based functional differential inclusion (FDI) theory is proposed. Under the framework of the Filippov state solution, the generalized Lyapunov functional method developed can obtain an indefinite time derivative almost anywhere along the system's state solutions. Some novel FNTS and FXTS analysis of the trivial state solution for FDI are provided. In particular, the settling time (ST) of FNTS/FXTS is presented. For the requirements of FNTS and FXTS, two control laws are designed for the discontinuous delayed neural networks (DNNs), respectively. Finally, the correctness and the advantages of the proposed method are demonstrated through its DNNs applications.