On Stability of Switched Linear Hyperbolic Conservation Laws with Reflecting Boundaries

摘要

We consider stability of an infinite dimensional switching system, posed as a system of linear hyperbolic partial differential equations (PDEs) with reflecting boundaries, where the system parameters and the boundary conditions switch in time. Asymptotic stability of the solution for arbitrary switching is proved under commutativity of the ad-vective velocity matrices and a joint spectral radius condition involving the boundary data.