Stability theory of differential equations

Abstract

<p>The problem of determining the stability of a set of linear differential equations has been of interest to mathematicians and engineers for a considerable length of time.</p> <p>The problem is attacked by obtaining the characteristic equation of the original set of equations and determining the stability of this equation.</p> <p>The stability of the characteristic equation is first considered in terms of a continued fraction expansion. Necessary and sufficient conditions are given for the characteristic equation to be stable.</p> <p>The stability of the equation is then determined by means of a determinant sequence, which was the manner originally presented by A. Hurwitz in 1895.</p> <p>The Nyquist criterion, which is a graphical method for determining whether the equation is stable, is then presented.</p> <p>An example is given for each of the above methods to illustrate the procedure used in determining whether the equation is stable or unstable. Also included is a brief analysis of stability for non-linear equations.</p>