TY - JOUR

T1 - On Leonov’s Method for Computing the Linearization of Transverse Dynamics and Analyzing Zhukovsky Stability

AU - Shiryaev, A. S.

AU - Khusainov, R. R.

AU - Mamedov, Sh N.

AU - Gusev, S. V.

AU - Kuznetsov, N. V.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - Abstract: The paper focuses on a comprehensive discussion of G. A. Leonov’s results aimed at analyzing the Zhukovsky stability of a solution to a nonlinear autonomous system by linearization. The main contribution is deriving the linear system that approximates dynamics of the original nonlinear systems transverse to the vector-flow on a nominal behavior. As illustrated, such a linear comparison system becomes instrumental in the analysis and re-design of classical feedback controllers developed previously for the stabilization of motions of nonlinear mechanical systems.

AB - Abstract: The paper focuses on a comprehensive discussion of G. A. Leonov’s results aimed at analyzing the Zhukovsky stability of a solution to a nonlinear autonomous system by linearization. The main contribution is deriving the linear system that approximates dynamics of the original nonlinear systems transverse to the vector-flow on a nominal behavior. As illustrated, such a linear comparison system becomes instrumental in the analysis and re-design of classical feedback controllers developed previously for the stabilization of motions of nonlinear mechanical systems.

KW - moving Poincaré section

KW - transverse linearization

KW - Zhukovsky stability

UR - http://www.scopus.com/inward/record.url?scp=85077058664&partnerID=8YFLogxK

U2 - 10.1134/S1063454119040071

DO - 10.1134/S1063454119040071

M3 - Article

AN - SCOPUS:85077058664

VL - 52

SP - 334

EP - 341

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -