A Lyapunov-Based Small-Gain Theorem for a Network of Finite-Time Input-to-State Stable Systems

• 成果类型: Article
• 署名作者: Li, Huanhuan; Liu, Tengfei; Jiang, Zhong-Ping
• 署名单位: Northeastern University - China; New York University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3274880
• 发表日期: 2024
• 页码: 1052-1059
• 关键词: Finite-time input-to-state stability (FTISS); Lyapunov functions; small-gain theorem

摘要

This article presents a Lyapunov formulation of the small-gain theorem for the finite-time input-to-state stability (FTISS) of an interconnected nonlinear system composed of two or more FTISS subsystems. In addition, an FTISS-Lyapunov function for the interconnected system is constructed from the FTISS-Lyapunov functions of the subsystems. With respect to the previously developed nonlinear, Lyapunov-based small-gain theorem restricted to input-to-state stability, a new power-function-based scaling technique is proposed to deal with the challenge that a nonlinearly scaled FTISS-Lyapunov function may not retain a decreasing rate as a power function with a positive power less than one.