Polynomial Transformation of Nonlinear Systems with Application to Stability Estimation
by
Vitaly G. Melnikov
St.-Petersburg Institute of Fine Mechanics and Optics, St.-Petersburg,Sablinskaya 14, 197101, Russia.

This paper presents a new method of polynomial transformations for nonlinear dynamic systems. Important is that the new method does not demand the definition of roots for a linear parts of the systems and does not lead to systems with complex variables. The method uses Lancszos procedure to minimize remainder terms. The main attention is focused on a nonspecial case and on a case of systems with nonlinear odd-functions characteristics. Application of the developed method to Lyapunov functions construction problem and to the nonlinear system stability estimation problem are considered.

Date received: March 11, 2003