Teaching linear systems theory using Cramer's rule

Abstract

A pedagogical approach based upon Cramer's rule is outlined for the presentation of linear systems theory in a first course for engineering students. The Laplace complex variable, or the Heaviside derivative operator, is used with Cramer's rule from elementary mathematics to allow students to expeditiously gain a foothold on linear dynamic systems theory. The approach applies to the broad class of finite-dimensional linear time invariant systems as they can be readily expressed as a square system of equations in the form Ax=Bu. The elements of the system's A and B matrices are, in general, polynomials in the Laplace complex variable or the Heaviside derivative operator. Cramer's rule permits an explicit solution for this square nonhomogeneous system for a desired unknown, or output, with respect to an input of interest. Consequently, Cramer's rule gives rise to a general method with pedagogical appeal for obtaining desired system transfer functions. The computational tasks may be done initially by hand and then by appropriate software as problems of greater complexity are examined. >