Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

In this paper, fixed-time stability problem of nonlinear system is investigated. Firstly, a new fixed-time stability theorem is established, and a higher precise estimate of settling time is provided. Secondly, by theoretical deduction, the provided estimate is compared with the ones in existing fixed-time stabiity theorems. It is shown that our estimate is less conservative and more accurate than existing results. Moreover, as a practical application, fixed-time stabilization problem of general neural networks is studied. By developing a framework of protocol and applying the new fixed-time stability theorem, some new criteria are derived to solve fixed-time stabilization problem of general neural networks systems. Finally, two simulation examples are provided to verify the validity of our theoretical results.