Stabilization of invariant sets for nonlinear systems with applications to control of oscillations (Q2716788)

The first statement on the stability of sets or partial stability problem was given by Lyapunov. Later such problems were intensively studied in Russia. Most results exploit properties of a known scalar function V (Lyapunov function). However, finding a Lyapunov function V is extremely difficult in general. One of a few powerful methods of constructing V-function is known as ``Chetaev's method of Bundles of First Integrals''.NEWLINENEWLINENEWLINEIn this paper, an analog of Chetaev's method is developed for partial stabilization (design) problems. In addition (to overcome some difficulties which arise when investigating a closed-loop system) the concept of V-detectability (introduced in a previous paper by one of the authors) is employed. A number of existing results on stabilization of invariant sets for nonlinear systems are overviewed and extended. Applications to the control of oscillations in pendulum, cart-pendulum and spherical pendulum systems are presented.