Energy Representation of Some Systems Described by Ordinary Differential Equations

Abstract

This paper describes a method of assigning energy to an ordinary differential equation. A linear differential equation of the n th order is assumed and also simple nonlinear example. The n th order equation can be converted into various versions of the state representations as n first-order equations. Though, usually these versions are not suitable for expressing energy. However, one version of the state space description is presented here - the energy representation that allows energy to be assigned to state variables. Finding the Lyapunov function and thus information about stability is also related to the energy and power description. But, it is generally necessary to transform the differential equation into the energy representation. The method of transformation is described in the paper and examples are also given. The results were calculated in Matlab.