POWER SERIES METHOD AND ASYMPTOTIC METHOD FOR THE STABILITY OF LINEAR SYSTEMS WITH TIME VARYING COEFFICIENTS

This paper deals with the application of power series and the asymptotic methods in investigating the stability of a linear control system with time varying coefficients. Instead of following the conventional method of handling a time variant system wherein, the given nth order differential equation is converted into a system of n-first order equations and then applying a suitable theory for examining its behavior, in this paper the power series method or the asymptotic method is applied. A suitable one among these methods is chosen depending on the nature of the point at infinity, with respect to the given differential equation. If the point at infinity is an irregular singular point, the asymptotic method is applied and if it is an ordinary or a regular singular point, the power series method is used to find an expression for the solutions at infinity. Basing on the behavior of these solutions, the stability of the given system can be inferred. In the course of this study, a few findings have been recorded that help to predict the behavior of a control system without completely finding the solution of its governing differential equation.