Hyperexponential and Fixed-Time Stability of Time-Delay Systems: Lyapunov-Razumikhin Method

• 成果类型: Article
• 署名作者: Nekhoroshikh, Artem N.; Efimov, Denis; Polyakov, Andrey; Perruquetti, Wilfrid; Furtat, Igor B.
• 署名单位: ITMO University; Universite de Lille; Centrale Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Inria; Universite de Lille; Centrale Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Russian Academy of Sciences
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3168487
• 发表日期: 2023
• 页码: 1862-1869
• 关键词: Stability criteria; Numerical stability; asymptotic stability; Symmetric matrices; Lyapunov methods; Linear matrix inequalities; transient analysis; Fixed-time and hyperexponential stability; implicit theorem; Linear matrix inequalities (LMIs); Lyapunov-Razumikhin theorem; time-delay systems

摘要

Razumikhin-like theorems on hyperexponential and fixed-time stability of time-delay systems are proposed for both explicitly and implicitly defined Lyapunov functions. While the former method is useful for stability analysis, the latter approach is more suitable for control synthesis. Examples of systems that can be stabilized hyperexponentially and in fixed time are given. The control parameters tuning algorithm is presented in the form of linear matrix inequalities. The numerical simulations illustrate the theoretical results.