About structure preserving feedback of controlled contact systems

The conditions for structure preserving feedback of controlled contact system are studied. It is shown that only a constant feedback preserves the canonical contact form, hence a structure preserving feedback implies a contact system with respect to a new contact form. A necessary condition is stated as a matching equation in the feedback, the contact vector fields, the canonical contact form and the closed-loop contact form. Furthermore, for the case of strict contact vector fields a set of solutions is characterized for a particular class of feedback and the relation with classical results on feedback control of Hamiltonian control systems is established. The control synthesis is briefly addressed and illustrated on a simple example.