Adaptive finite‐time stabilization of stochastic nonlinear systems with the powers of positive odd rational numbers

AbstractSummaryIn this paper, we give some new results on finite‐time stabilization for stochastic nonlinear systems whose powers of integrators are all positive odd rational numbers (ie, numerators and denominators of the powers are all positive odd integers) but not necessary only high order or low order. By adopting new conditions on drift and diffusion terms, Lyapunov function, and controller design method, a state feedback controller is designed to guarantee stochastic nonlinear systems finite‐time stable in probability. Moreover, when unknown parameters exist in systems, we give the adaptive finite‐time state feedback controller. Numerical examples demonstrate the effectiveness of the proposed results.