A Method to Optimize the Stability of a Linear Dynamic System

Abstract

A systematic and numerical procedure is described for optimizing the stability of a linear dynamic system. The process is an application of the so-called “steepest-descent method”, and since the stability of a linear dynamic system is determined by the real part of the roots of the characteristic equation, the practical procedure is suggested in this paper. A numerical example is presented for maximizing the damping of the perturbed motion of a earth satellite by the use of the gravity-oriented principle.