On stability of nonlinear hyperbolic systems with reaction and switching

This paper investigates the exponential stability in L² norm of scalar nonlinear hyperbolic systems of balance laws with the reaction that may be accumulative or dissipative. Two Lyapunov-based stability criteria that depend on the system parameters and boundary data are proposed with fully considering the reactions´ characteristics. The new results can help to construct a common Lyaunov function to stabilize the switched nonlinear hyperbolic systems under arbitrary switching. Several traffic system examples are taken to illustrate the theoretical results.