Zuyev O. Stabilization and stability of nonlinear dynamical systems with application to the problems of rigid bodies mechanics.

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0400U002416

Thesis Registration Form

0400U002416.pdf

Applicant for

Specialization

  • 01.02.01 - Теоретична механіка

20-09-2000

Specialized Academic Board

Д 11.193.01

Essay

It is proved, that for any locally controllable system there exists a discontinuous feedback control ensuring stability of the origin. The asymptotic estimates of solutions of the model system are obtained for the critical case of two pairs of purely imaginary roots. Theorems on partial stabilization of nonlinear systems are proved in terms of control Lyapunov functions. With the help of these results the problems on partial stabilization of the orientation of a rigid body by means of a pair of control torques are solved. A mathematical model of the wind engine is constructed, the conditions of stability of uniform rotations are investigated.

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