Stabilization in Distribution by Delay Feedback Control for Hybrid Stochastic Differential Equations

• 成果类型: Article
• 署名作者: You, Surong; Hu, Liangjian; Lu, Jianqiu; Mao, Xuerong
• 署名单位: Donghua University; University of Strathclyde
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3075177
• 发表日期: 2022
• 页码: 971-977
• 关键词: Feedback control; Markov processes; control systems; DELAYS; asymptotic stability; Stability criteria; Symmetric matrices; Brownian Motion; delay feedback control; Markov chain; stability in distribution

摘要

This article is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilization in distribution). This is the first article in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilization in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design feedback controls in two structure cases: state feedback and output injection.