High-Gain Observer Design for a Class of Quasi-Linear Integro-Differential Hyperbolic Systems-Application to an Epidemic Model

• 成果类型: Article
• 署名作者: Kitsos, Constantinos; Besancon, Gildas; Prieur, Christophe
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3063368
• 发表日期: 2022
• 页码: 292-303
• 关键词: C-1 exponential stability; high-gain observers; Lyapunov analysis; nonlocal terms; partial integro-differential equations (PIDEs); quasi-linear hyperbolic systems; SIR epidemic models

摘要

This article addresses the problem of high-gain observer design for a class of quasi-linear hyperbolic systems (with one characteristic velocity), possibly including nonlocal terms, making them systems of partial integro-differential equations. The design relies on distributed measurement of a part of the state vector. The observer is presented and discussed and the exponential stability in the C-1 spatial norm of the origin for the error system is fully established via Lyapunov-based analysis. Its use is illustrated via an application to an age-dependent susceptible, infected, recovered (SIR) epidemic model.