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

Abstract : This work 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 C1 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 SIR epidemic model.
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https://hal.archives-ouvertes.fr/hal-03152772
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Submitted on : Thursday, February 25, 2021 - 7:11:34 PM
Last modification on : Wednesday, January 5, 2022 - 3:50:12 AM
Long-term archiving on: : Wednesday, May 26, 2021 - 7:22:44 PM

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Constantinos Kitsos, Gildas Besancon, Christophe Prieur. High-Gain Observer Design for a Class of Quasi-linear Integro-Differential Hyperbolic Systems - Application to an Epidemic Model. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2022, 67 (1), pp.292 - 303. ⟨10.1109/TAC.2021.3063368⟩. ⟨hal-03152772⟩

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