Analysis of time delay systems

Abstract

Two methods are suggested for the analysis of second-order time delay systems. One of them is graphical and makes use of x" + ax' versus x and x" + bx versus x' planes (a and b are constants) for getting the time solution of certain second-order non-linear differential-difference equations (d.d.e.). The other method is analytical and is a modification of Poincare's perturbational series to obtain an explicit solution of d.d.e, in terms of the parameter associated with time delay terms. Also included is a variation of the double delta method for solving general second-order d.d.e. A comparison, in the end, of the methods shows the usefulness and simplicity of the proposed techniques.