Dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity-based control

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a technique that regulates the behavior of nonlinear systems assigning a desired (Port Hamiltonian) structure to the closed-loop. This basic idea, introduced seven years ago, has turned out to be very successful and has provided solutions to a wide variety of physical problems. Although IDA-PBC is originally formulated as a static state-feedback technique a natural question that arises is whether it is possible to extend the realm of applicability of the method by considering dynamic controllers. More precisely, is the set of plants that is stabilizable with static state-feedback IDA-PBC smaller than the one stabilizable with dynamic IDA-PBC? The main contribution of this paper is to prove that the answer to this question is, unfortunately, negative.