6533b825fe1ef96bd12826cd
RESEARCH PRODUCT
On Leonov’s method for computing the linearization of the transverse dynamics and analysis of Zhukovsky stability
Ramil KhusainovNikolay KuznetsovNikolay KuznetsovNikolay KuznetsovSh. N. MamedovA. S. ShiryaevSergei V. Gusevsubject
General Mathematics010102 general mathematicsLinear systemDynamics (mechanics)General Physics and Astronomy01 natural sciencesStability (probability)010305 fluids & plasmasNonlinear systemTransverse planeLinearizationControl theoryNonlinear mechanical systems0103 physical sciences0101 mathematicsAutonomous system (mathematics)Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-01 | Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy |