G. Bastin

Title: Lyapunov stability analysis of networks of conservation laws

Abstract :
We are concerned with physical networks described by systems of 1st-order (or scalar) and 2nd-order (or 2x2) conservation laws.  For such systems, the issue of the equilibrium stability (in the sense of Lyapunov) is addressed. It is shown that an entropy-based strict Lyapunov function can be used to prove the asymptotic (exponential) stability of the equilibria. The analysis gives a sufficient stability condition which is weaker than the condition previously known in the literature. The analysis is applied to the boundary feedback control problem which consists of designing control actions in order to guarantee that the system trajectories converge to a desired set-point. The approach is illustrated with an application to ramp-metering control of road traffic networks.