Lyapunov Functions and Controllers for the Global Stabilization of the Two and Three Dimensional Moore-greitzer Compressor Dynamics Models

In this paper, we nd all the Lyapunov functions that correspond to the stabilization of the two-dimensional MG model and discuss possible choices of controllers. We also give a complete treatment of the problem of only having positive control action available. For the three-dimensional model, we address the issue of whether the equilibrium point on the compressor characteristic is stabilizable or not and how a Lyapunov function (in the sense of a CLF) can be chosen. This leads to controllers more general than the S-controller derived recently. Throughout, we employ a geometric approach that makes the treatment of global control problems more natural and yields information on the transient behavior of trajectories (controlled or not.)