Stabilization of linear systems with multiple unknown time-varying input delays by linear time-varying feedback

作     者：Zhou, Bin Zhang, Kai 

作者机构：Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China Natl Key Lab Complex Syst Control & Intelligent Ag Harbin 150001 Peoples R China 

出 版 物：《AUTOMATICA》 (Automatica)

年 卷 期：2025年第174卷

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：State Council Ministry of Education of the People's Republic of China, MOE China National Funds for Distinguished Young Scientists National Natural Science Foundation of China, NSFC, (62188101, 62125303, U2441243, 62403163, 62173111) National Natural Science Foundation of China, NSFC Aeronautical Science Foundation of China, (2023Z034077002) Aeronautical Science Foundation of China Fundamental Research Funds for the Central Universities, (2022FRFK060018) Fundamental Research Funds for the Central Universities CPSF, (GZB20230956) 

主　　题：Unknown input delay Parametric Lyapunov equation Linear time-varying feedback Asymptotic stabilization 

摘      要：This paper addresses the stabilization of linear systems with multiple time-varying input delays. In scenarios where neither the exact delays information nor their bound is known, we propose a class of linear time-varying state feedback controllers by using the solution to a parametric Lyapunov equation (PLE). By leveraging the properties of the solution to the PLE and constructing a time-varying Lyapunov-Krasovskii-like functional, we prove that (the zero solution of) the closed-loop system is asymptotically stable. Furthermore, this result is extended to the observer-based output feedback case. The notable characteristic of these controllers is their utilization of linear time-varying gains. Furthermore, they are designed entirely independent of any knowledge of the time delays, resulting in controllers that are exceedingly easy to implement. Finally, a numerical example demonstrates the effectiveness of the proposed approaches. (c) 2025 Published by Elsevier Ltd.