Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the L² norm

2020/11/25 by Hayat, Amaury
#35F60 #35F61 #93D09 #93D15 #93D20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2011.12682

Abstract

In this paper we study the global exponential stability in the L² 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 L² norm with respect to both interior and boundary disturbances.

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