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

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.

arXiv comment29 pages, 1 figure

References in corpus (4)

• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment
• Boundary exponential stabilization of 1-D inhomogeneous quasilinear hyperbolic systems
• Approximate and exact controllability of linear difference equations
• An analysis of the input-to-state-stabilisation of linear hyperbolic systems of balance laws with boundary disturbances