Extension of Pozharitsky Theorem for partial stabilization of a system with several first integrals

The paper is devoted to an extension of one particular fact within theory of partial stability, the so-called Pozharitsky theorem, to the case of partial stabilization of nonlinear controlled system. It is shown that under appropriate assumptions partial stabilization of the system based on usage of some Lyapunov function constructed from first integrals of the unforced system, implies that the Lyapunov function of a simplified form also leads to a controller that partially stabilizes the system. The theoretical results are illustrated by the problem of partial stabilization of the downward equilibrium of the inertia wheel pendulum.