Abstract
This chapter deals with the robust stability analysis of a coupled system made up of an uncertain ordinary differential system and a string equation. The main result states the robust exponential stability of this interconnected system subject to polytopic uncertainties. The Lyapunov theory transforms the stability analysis into the resolution of a set of linear matrix inequalities. They are obtained using projections of the infinite dimensional state onto the orthogonal basis of Legendre polynomials. The special structure of these inequalities is used to derive robust stability results. An example synthesizes the two main contributions of this chapter: an extended stability result and a robustness analysis. The example shows the efficiency of the proposed method.
This work is supported by the ANR project SCIDiS contract number 15-CE23-0014.
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Barreau, M., Seuret, A., Gouaisbaut, F. (2022). Lyapunov Stability of a Coupled Ordinary Differential System and a String Equation with Polytopic Uncertainties. In: Valmorbida, G., Michiels, W., Pepe, P. (eds) Accounting for Constraints in Delay Systems. Advances in Delays and Dynamics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-89014-8_9
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