1. Finite-time stochastic integral input-to-state stability and its applications.
- Author
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Cui, Rong-Heng and Xie, Xue-Jun
- Subjects
- *
STOCHASTIC integrals , *STABILITY of nonlinear systems , *STOCHASTIC systems , *NONLINEAR systems , *CLOSED loop systems - Abstract
In this paper, finite-time stabilization is investigated in depth for stochastic nonlinear systems with stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: (i) Motivated by the concept of stochastic integral input-to-state stability (SiISS) and the existing stochastic finite-time stability theorem, a new concept of finite-time stochastic integral input-to-state stability (FT-SiISS) using Lyapunov function is first introduced, and an inclusion relationship among three types of stochastic stability, i.e., FT-SiISS, FT-SISS and SISS, is rigorously established. On the basis of FT-SiISS, we develop two new FT-SiISS small-gain conditions and discuss their relationship. Then, to analyze finite-time stability of stochastic nonlinear systems with FT-SiISS inverse dynamics, a stochastic finite-time stability theorem is improved. (ii) As the application of (i), we propose a unified finite-time control method, which can simultaneously handle stochastic nonlinear systems with FT-SiISS or FT-SISS inverse dynamics, and guarantee that the closed-loop system has an almost surely continuous solution, all the closed-loop signals are bounded almost surely, and its trivial solution is stochastically finite-time stable. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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