Attracting ellipsoids and synthesis of oscillatory regimes

An approach to stabilization of nonlinear oscillations in multidimensional spaces is proposed on the basis of the V.I. Zubov’s stability theory for invariant sets. As a special case, the derived controls make it possible to excite self-oscillating regimes in specified state subspaces R ^2k ? R ²ⁿ with simultaneous oscillation damping on Cartesian products R ^2n?2k .