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

Amaury Hayat

doi:10.1016/j.sysconle.2020.104848

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

Amaury Hayat

Rutgers University–Camden

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	104848
Journal	Systems and Control Letters
Volume	148
DOIs	https://doi.org/10.1016/j.sysconle.2020.104848
Publication status	Published - 1 Feb 2021

Keywords

Global stabilization
Hyperbolic systems
Inhomogeneous
Lyapunov
Nonlinear
Nonlocal

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10.1016/j.sysconle.2020.104848

Cite this

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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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AB - 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.

KW - Global stabilization

KW - Hyperbolic systems

KW - Inhomogeneous

KW - Lyapunov

KW - Nonlinear

KW - Nonlocal

UR - https://www.scopus.com/pages/publications/85098141069

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JO - Systems and Control Letters

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ER -

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

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Keywords

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