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.
Talk