Laplace's analyses for application of π circuits' associations in digital simulations

Searching for better results, the classic mathematical tools and theorems of dynamic control theory are applied to the analyses of the numeric routine for electrical transients' digital simulations. This numeric routine solves the linear system that represents the π circuits' cascade. So, the differential equations of this system are analyzed using Laplace's transform and, based on these analyses, the numeric routine is changed, leading to more accurate results than those obtained using only one matrix for representing the π circuits' cascade in state equations.