Exponential stability of boundary control port Hamiltonian systems with dynamic feedback.

International audienceIn this paper it is shown that an input strictly passive linear finite dimensional port-Hamiltonian controller exponentially stabilizes a large class of boundary control systems. This follows since the finite dimensional controller dissipates the energy owing through the boundaries of the infinite dimensional system. The assumptions on the controller is that it is input strictly passive and that it is exponentially stable. The result is illustrated on the model of a DNA-manipulation process, that is used to show that the interconnection of the DNA-bundle+the controller (finite dimensional part of the system) and a micro-gripper (infinite dimensional part) is exponentially stable