  In this paper, we analyse the behaviour of a buck converter network that
contains arbitrary, up to mild regularity assumptions, loads. Our analysis of
the network begins with the study of the current dynamics; we propose a novel
Lyapunov function for the current in closed-loop with a bounded integrator. We
leverage on these results to analyse the interaction properties between
voltages and bounded currents as well as between node voltages and to propose a
two-layer optimal controller that keeps network voltages within a compact
neighbourhood of the nominal operational voltage. We analyse the stability of
the closed loop system in two ways: one considering the interconnection
properties which yields a weaker ISS type property and a second that
contemplates the network in closed loop with a distributed optimal controller.
For the latter, we propose a novel distributed way of controlling a Laplacian
network using neighbouring information which results in asymptotic stability.
We demonstrate our results in a meshed topology network containing 6 power
converters, each converter feeding an individual constant power load with
values chaning arbitrarily within a pre-specified range.

Systems and Control;Systems and Control