Finite-time stability and stabilization of highly nonlinear stochastic systems via the noise control

This paper provides a new perspective for the stability analysis of highly nonlinear stochastic systems, including stochastic finite-time (FT) stability, stochastic fixed-time (FIXT) stability, and stochastic predefined-time (PT) stability. Compared with other relevant literature, we explicitly demonstrate the beneficial effects of stochastic terms on these stabilities, and significantly enhance the differential operator conditions of the Lyapunov function by utilizing them. Additionally, we provide sufficient conditions for the instability of highly nonlinear stochastic systems. Finally, unlike previous control methods, we propose a class of stochastic control methods that guarantee stochastic PT stability, clearly illustrating that both the drift and diffusion coefficients can be highly nonlinear.