A Numerical Method for Solving Time-Invariant System by Generalized Inverse Vandermonde Matrix

A simple numerical algorithm based on the generalized Inverse Vandermore matrix for evaluation of time response to a time-invariant system is proposed. The system is assumed to be governed by a high order linear differential equation with constant coefficients. The technique involves determination of the partial-fraction expansion of rational functions. Only synthetic division and longhand division are required, which makes the process very suitable for computer programming. Meanwhile, because the solution is directly related to the systemís initial conditions, the proposed approach only requires computation of the inverse generalized Vandermonde matrix.