Uniformity of Controllability and Stabilization of Switched Linear Time-Varying Systems

• 成果类型: Article
• 署名作者: Wang, Xingping; Chi, Dianwei
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3389568
• 发表日期: 2024
• 页码: 6429-6434
• 关键词: Switches; CONTROLLABILITY; Switched systems; Lyapunov methods; State feedback; Linear systems; indexes; Average dwell time; stabilization; switched linear time-varying systems; transition matrix; uniformity of controllability

摘要

We consider the stabilization of systems that switch among an arbitrary number of linear time-varying subsystems, which cannot be stabilized by simply stabilizing all the subsystems even if their dwell time is large enough. We introduce a uniformity condition on the controllability of all the subsystems under which we can design controllers for the subsystems such that the closed-loop subsystems are exponentially stable, and their state transition matrices have uniformly bounded magnitudes. We prove using this uniformity condition that the systems considered are exponentially stabilizable if the switching signals have a known or unknown positive average dwell time.