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

Abstract

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C^1$</tex-math></inline-formula> 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.