On the Accuracy of Quadrature Laplace Transform Inversion and the Solution of State Space Equations

Abstract

A quadrature formula is shown to be an approximation of the power-series method of inverting Laplace transforms. This together with the properties of the constants derived from a power-series expansion of the Padé approximation to exp (s) yield an important upper limit on t which is quite sharp in determining the breakdown point up to and after which the approximation is accurate and inaccurate respectively. The solution of state space equations using the quadrature inversion formula is also discussed