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

Abstract — It is well known that if the linear time invariant system x ̇ = Ax + Bu, y = Cx is passive the associated incremental system ˙̃x = Ax ̃ + Bũ, y ̃ = Cx̃, 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 x ̇ = f(x) + gu, y = h(x) whose incremental model is also passive. Using this result we then prove that general nonlinear RLC circuits with convex and proper electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear PI control. I. PROBLEM FORMULATION In many control applications one is interested in operating the system around a non–zero equilibrium point. A standard procedure to describe the dynamics in these cases is t