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arXiv · 2103.15747

Well-posedness and robust stability of a nonlinear ODE-PDE system

S. Dashkovskiy·O. Kapustyan·V. Slynko
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Abstract

This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we develop an approach for a construction of a suitable coercive Lyapunov function as one of the main results. Based on this Lyapunov function we establish the well-posedness of the considered system and establish conditions that guarantee the ISS property. ISS estimates are derived explicitly for the particular case of globally Lipschitz nonlinearities.

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S. Dashkovskiy, O. Kapustyan, V. Slynko. 2021-03-29. Well-posedness and robust stability of a nonlinear ODE-PDE system. https://arxiv.org/abs/2103.15747

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