LAUSR

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.