Stability of Stochastic Functional Differential Equations With Past-Dependent Random Switching Involving Countably Infinite States

• 成果类型: Article
• 署名作者: Nguyen, Dang H.; Nguyen, Nhu N.; Ta, Trang T.; Yin, George
• 署名单位: University of Alabama System; University of Alabama Tuscaloosa; University of Rhode Island; University of Connecticut
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3326362
• 发表日期: 2024
• 页码: 1612-1626
• 关键词: Switches; Differential equations; HISTORY; Stability criteria; mathematical models; DELAYS; Numerical stability; Past-dependent switching; STABILITY; stochastic functional differential equation (SFDE)

摘要

This work is devoted to stochastic functional differential equations with past-dependent random switching, in which the switching process is allowed to take values in a countable state space. Such processes are rather versatile and arise in a wide variety of applications. A central issue considered in this article is stability. The conditions provided are more general than the existing work. After getting the desired stability results, several applications, including linear systems, linearization of nonlinear systems, multi-agent systems consentability, and networked control systems are examined. Numerical results are also provided to demonstrate our results.