A new theorem on finite‐time stability of stochastic homogeneous systems and its application

This paper provides a novel Lyapunov theorem on finite‐time stability of stochastic homogeneous systems. Different from the existing results, the differential operator LV$$ \mathcal{L}V $$ in this paper is not required to be negative definite and could be negative semidefinite. The obtained condition is somehow similar to the LaSalle's condition. Moreover, the existing theorem of finite‐time stability for stochastic homogeneous systems is a special case of our result. As an application of the obtained theorem, stochastic finite‐time stabilization is considered for stochastic homogeneous affine control systems. Some examples and simulations are provided to show the effectiveness of the results.