This article is cited in 1 paper

Analysis and synthesis of control systems

Decomposition of the vector field of control system by constructing a homotopy operator

S. N. Chukanov^a, D. V. Ulyanov<sup>b

a</sup> Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Omsk State Technical University

Abstract: The method for decomposition of the vector field of a dynamical system based on construction of homotopy operator is proposed. The vector fields of dynamical systems can be classified on the basis of SVD-decomposition of potential components of the vector field. The method of decomposition of dynamical system vector field is used to construct Lyapunov functions for control systems.

Keywords: vector field decomposition, control system, Lyapunov function, Hodge–Helmholtz decomposition, operator of homotopy.

UDC: 519.71