Passivity of nonlinear incremental systems:Application to PI stabilization of nonlinear RLC circuits

It is well known that if the linear time invariant system is passive the associated incremental system , with , u,y the constant input and output associated to an equilibrium state x, is also passive. In this paper, we identify a class of nonlinear passive systems of the form whose incremental model is also passive. Using this result we then prove that a large class of nonlinear RLC circuits with strictly convex electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear PI control. Keywords: Passivity; Incremental models; Nonlinear system