On Leonov’s method for computing the linearization of the transverse dynamics and analysis of Zhukovsky stability

Abstract

The paper is focused on a comprehensive discussion of one of results of Prof. G. A. Leonov aimed at analysis of Zhukovsky stability of a solution of a nonlinear autonomous system by linearization. The main contribution is in deriving a 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 analysis and re-design of classical feedback controllers developed earlier for stabilization of motions of nonlinear mechanical systems.