A New Design to Finite-Time Stabilization of Nonlinear Systems With Applications to General Neural Networks

Abstract

The finite-time stabilization problem of nonlinear systems is investigated in this paper. Firstly, to improve the precision of settling time of nonlinear system, a new finite-time stability theorem is established, and a higher precision settling time is derived from it. Moreover, by theoretical derivation, we prove that the corresponding settling time is more accurate than the existing results. Secondly, as an application, a new class of finite-time protocol framework, which unifies continuous protocol and discontinuous ones into a uniform formula, is designed to solve the finite-time stabilization problem of the general neural network system, and it can bring to a continuous control protocol and a discontinuous control protocol through choosing different design parameters. It is shown that the convergence rate is improved and also the corresponding settling time is upper bounded by some positive constant independent of initial conditions, which makes it convenient and flexible to adjust the settling time by adjusting design parameters. Finally, two numerical examples are provided to illustrate the effectiveness of our theoretical results. INDEX TERMSFinite-time stability theorem; Filippov solution; General neural networks; Lyapunov function; Settling time function; Upper bound of settling time