Filippov's Solution and Finite-Time Stability of Stochastic Systems for Discontinuous Control

• 成果类型: Article
• 署名作者: Chen, Sheng; Li, Tao; Zang, Qiang; Liu, Yunping
• 署名单位: Nanjing University of Information Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3190962
• 发表日期: 2023
• 页码: 3348-3361
• 关键词: Indium tin oxide; Synchronization; Stability criteria; Stochastic systems; Stochastic processes; Sliding mode control; Particle measurements; stochastic system; finite-time stability; neural synchronization; solution existence; stochastic differentiation

摘要

this article, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov's solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical Ito differentiation formula is generalized for quasi-C?(2)(0) (R-n, R)-class functions along Filippov's solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite time stability results of stochastic differential systems are revealed with Filippov's solutions, and one of them is applied to neural synchronization, together with case simulations.