Constructive interconnection and Damping Assignment for port-controlled Hamiltonian

The Interconnection and Damping Assignment passivity-based control method for port-controlled Hamiltonian systems is discussed. We propose a novel construction which exploits the notion of algebraic solution of the so-called matching equation. The latter notion is instrumental in constructing an energy function defined on an extended state-space without involving the solution of any partial differential equation. This results, differently from the classical solution, in a dynamic state feedback that stabilizes a desired equilibrium point. Finally we show that, in the linear time-invariant case and under standard assumptions, the proposed methodology provides the standard passivity-based controller.