Proportional plus integral control for set-point regulation of a class of nonlinear RLC circuits

In this note we identify graph-theoretic conditions which allow to write a nonlinear RLC circuit as port-Hamiltonian with constant input matrices. We show that under additional monotonicity conditions on the networks components, the circuit enjoys the property of relative passivity, an extended notion of classical passivity. The property of relative passivity is then used to build simple, yet robust and globally stable, Proportional plus Integral controllers.