Prescribed-time stabilization control for p-norm stochastic nonlinear systems based on homogeneous dominant technique

In this article, a prescribed-time state-feedback stabilization design strategy is proposed for a class of p-norm stochastic nonlinear strict feedback systems. In previous work on prescribed-time stabilization of stochastic systems, only stochastic nonlinear systems with fractional power less than or equal to one are considered. To overcome this problem, we improve the existing method and discuss the issue of prescribed-time stabilization of stochastic nonlinear systems with fractional power is arbitrary positive odd rational number. First, a prescribed-time controller is designed by combining the Lyapunov function with adding a power integrator technique. It should be pointed out that the homogeneous domination approach is adopted when dealing with the nonlinear terms of the system. Then, according to the stochastic prescribed-time stability theorem, it is proved that the designed controller can ensure the closed-loop system is prescribed-time mean-square stable. Finally, three simulation examples are given to investigate the validity of the presented method, in which the last one is an electromechanical system example.