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

In English The paper is devoted to an extension of one particular fact withintheory 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 partialstabilization of the system based on usage some Lyapunov functionconstructed from first integrals of the unforced system, impliesthat the Lyapunov function of a simplified form also leads toa controller that partially stabilizes the system. The theoreticalresults are illustrated by the problem of partial stabilization ofthe downward equilibrium of the Inertia Wheel Pendulum.