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

It is well known that if the linear time invariant system \dot x=Ax+Bu, y=Cx is passive the associated incremental system \dot \tilde x=A \tilde x+B \tilde u, \tilde y=C \tilde x,with \tilde(·)=(·)−(·)^\star, u^\star, y^\star the constant input and output associated to an equilibrium state x^\star, is also passive. In this paper, we identify a classof nonlinear passive systems of the form \dot x = f(x) + gu, y = h(x) whose incremental model is also passive. Using this result we then provethat a large class of nonlinear RLC circuits with strictly convex electric and magnetic energy functions and passive resistors with monotoniccharacteristic functions are globally stabilizable with linear PI control