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.

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