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

Héctor Ramirez Estay (1) , Hans Zwart (2) , Yann Le Gorrec (1)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 University of Twente

In 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.

Domaines: Micro et nanotechnologies/Microélectronique

Héctor Ramirez Estay, Hans Zwart, Yann Le Gorrec. Exponential stability of boundary control port Hamiltonian systems with dynamic feedback.. First IFAC Workshop on Control of Systems Modeled by Partial differential Equations, CPDE'13., Jan 2013, France. pp.1-7. ⟨hal-00872199⟩