Stabilization of nonlinear system with limiting set in the form of a triangle. (Russian) Zbl 1249.70029

Grushkovskaya, V. V.; Zuev, A. L.

Tr. Inst. Prikl. Mat. Mekh. 19, 53-64 (2009).

The problem of stabilization of position of balance of system of the Euler equations with limitation on the operating moment from set in the form of a triangle is considered in this work. Conditions asymptotical stability of nonlinear system are found in terms of invariants concerning transformations with feedback. In the course of the solution the theory of critical Hamiltonians with which help the necessary condition of stabilization of system is found is applied. Feedback function is constructed for a considered problem. The basic result of work is the sufficient conditions of stabilization the considered system.

Reviewer: R. I. Manuilenko

MSC:

70H14

Stability problems for problems in Hamiltonian and Lagrangian mechanics