Stability and L1-Gain Analysis of Periodic Piecewise Positive Systems With Constant Time Delay

• 成果类型: Article
• 署名作者: Zhu, Bohao; Lam, James; Xie, Xiaochen; Song, Xiaoqi; Kwok, Ka-Wai
• 署名单位: University of Hong Kong; The University of Hong Kong Shenzhen Institute of Research & Innovation; University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3089640
• 发表日期: 2022
• 页码: 2655-2662
• 关键词: L-1-gain analysis; periodic systems; positive systems; stability analysis; time-delay systems

摘要

This article is concerned with the stability and L-1-gain analysis of periodic piecewise positive systems with constant time delay. lambda-exponential stability, which is applied to characterize the decay rates of the considered systems, is investigated first. A copositive Lyapunov-Krasovskii functional is used to obtain a sufficient stability condition. The stability condition characterizes the convergent speed of the state by the system matrices and the size of the time delay. One can also apply the Lyapunov-Krasovskii functional to characterize the L-1-gain of the systems. By taking advantage of the periodic property of the system, linear inequalities are employed to characterize the L-1-gain, and an unweighted upper bound of the L-1-gain of the system is given.