Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm

Amaury Hayat

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arXiv · 2011.12682

Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm

Amaury Hayat

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Abstract

In this paper we study the global exponential stability in the $L^{2}$ norm of semilinear $1$-$d$ hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient stability conditions: an internal condition and a boundary condition. This result holds also when the source term is nonlocal. Finally, we show its robustness by extending it to global Input-to State Stability in the $L^{2}$ norm with respect to both interior and boundary disturbances.

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Amaury Hayat. 2020-11-25. Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm. https://arxiv.org/abs/2011.12682

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