  We provide a constructive method designed in order to control the stability
of a given periodic orbit of a general completely integrable system. The method
consists of a specific type of perturbation, such that the resulting perturbed
system becomes a codimension-one dissipative dynamical system which also admits
that orbit as a periodic orbit, but whose stability can be a-priori prescribed.
The main results are illustrated in the case of a three dimensional dissipative
perturbation of the harmonic oscillator, and respectively Euler's equations
form the free rigid body dynamics.
