Lyapunov functions for switched linear hyperbolic systems*

Systems of conservation laws and systems of balance laws are considered in this paper. These kinds of infinite dimensional systems are described by a linear hyperbolic partial differential equation with and without a linear source term. The dynamics and the boundary conditions are subject to a switching signal that is a piecewise constant function. By means of Lyapunov techniques some sufficient conditions are given for the exponential stability of the switching system, uniformly for all switching signals. Different cases are considered depending on the presence or not of the linear source term in the hyperbolic equation, and depending on the dwell time assumption on the switching signals. Some numerical simulations are also given to illustrate some main results, and to motivate this study.