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

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 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. Key words: Passivity, incremental models, nonlinear systems