Defining of Lyapunov Functions for the Generalized Nonlinear Object

Abstract

The paper d eals with the development of a method for defining of Lyapunov functions. This method is based on usage of coordinate transformations for both linear and nonlinear dynamical objects. One can use proposed method for definition of Lyapunov functions, which can be used as a basis for stability analysis. Positiveness and continuity of the above-mentioned functions are guaranteed by using the complete square technique while coefficients of Lyapunov functions are defined. Lyapunov functions which are defined into such way can be converted into various state spaces. Such transformation allows us to get non-quadratic Lyapunov functions for nonlinear dynamic objects and quadratic for linear ones. While one use Lie derivatives for performing coordinate transformation he can reduce the order of Lyapunov function, which is obtained for a controllable dynamical object.