Finite‐time stabilization of stochastic nonlinear systems with SiISS inverse dynamics

Summary This paper investigates the finite‐time control problem for a class of stochastic nonlinear systems with stochastic integral input‐to‐state stablility (SiISS) inverse dynamics. Motivated by finite‐time stochastic input‐to‐state stability and the concept of SiISS using Lyapunov functions, a novel finite‐time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite‐time SiISS small‐gain arguments, using the backstepping technique and stochastic finite‐time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state‐feedback controller that can ensure the solution of the closed‐loop system to be finite‐time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.