Robust stability of a nonlinear ODE-PDE system. (English) Zbl 1518.35064
Summary: 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 construction of a suitable coercive Lyapunov function as one of our main results. Based on this Lyapunov function, we establish well-posedness of the considered system and establish conditions that guarantee the input-to-state stable (ISS) property. ISS estimates are derived explicitly for the particular case of globally Lipschitz nonlinearities.
MSC:
| 35B35 | Stability in context of PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K58 | Semilinear parabolic equations |
| 37L15 | Stability problems for infinite-dimensional dissipative dynamical systems |
| 93D09 | Robust stability |
| 93D20 | Asymptotic stability in control theory |
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