  Dynamical stabilization processes (homeostasis) are ubiquitous in nature, but
energetic resources needed for their existence were not studied systematically.
Here we undertake such a study using the famous model of Kapitza's pendulum,
which attracted attention in the context of classical and quantum control. This
model is generalized and made autonomous. We show that friction and stored
energy stabilize the upper (normally unstable) state of the pendulum. The upper
state can be made asymptotically stable and yet it does not cost any constant
dissipation of energy, only a transient energy dissipation is needed. The
asymptotic stability under a single perturbation does not imply stability with
respect to multiple perturbations. For a range of pendulum-controller
interactions, there is also a regime where constant energy dissipation is
needed for stabilization. Several mechanisms are studied for the decay of
dynamically stabilized states.
