Fixed-Time Stabilization of Leakage-Delayed Neural Networks Modeled by Delayed Filippov Systems: Leakage-Delay-Dependent Settling-Time

This paper considers the periodicity and fixed-time stabilization of discontinuous neural networks with time-varying leakage and discrete delays, which is more general. Before considering the stability, the existence of periodic solutions in the sense of Filippov should be proved. So, firstly, based on the set-valued mapping, coincidence theorem, Holder inequality and supremum-infimum principle, the investigation on the leakage-delay-dependent periodic solutions is obtained, which can not only complement the periodic solutions of leakage-delayed neural networks, but also is absolutely different from the almost-periodic solution results. Secondly, by virtue of the integral inequality, new fixed-time stability lemmas of Filippov systems are established, which involve more relaxed assumptions and do not need to input extra parameters. Thirdly, leakage-delay-dependent results on fixed-time stabilization of the proposed neural networks are established via the new fixed-time stability lemmas under modified non-chattering control laws. It is worth mentioning that the settling-times are relevant to the leakage delays, which have not been reported in the literature. Finally, the validity of the proposed results is demonstrated by two numerical examples.

Automated summary

This paper examines the periodicity and fixed-time stabilization of discontinuous neural networks with time-varying leakage and discrete delays, which is a more general case. Firstly, the study on leakage-delay-dependent periodic solutions is achieved through set-valued mapping, coincidence theorem, Holder inequality, and supremum-infimum principle. Secondly, new fixed-time stability lemmas of Filippov systems are established by using integral inequality, which have relaxed assumptions and do not require additional parameters. Thirdly, leakage-delay-dependent results on fixed-time stabilization of the proposed neural networks are obtained under modified non-chattering control laws based on the new stability lemmas. The validity of the proposed results is demonstrated through numerical examples.