Dynamic Interconnection and Damping Assignment

The Interconnection and Damping Assignment passivity-based control method for port-controlled Hamiltonian systems is discussed. We propose a new definition of algebraic solution of the so-called matching equation. This notion is instrumental for the construction of an energy function on an extended state-space, which does not rely on the solution of any partial differential equation. We provide sufficient conditions that allow to preserve the port-Hamiltonian structure in the extended closed-loop system. The theory is validated on an electrostatic microactuator by assigning an interconnection and damping structure that cannot be imposed with the standard approach.