Numerically reliable software for control: the SLICE library

The algorithms developed in the control literature have generally been devised from a purely theoretical viewpoint, with no attention being paid to the numerical difficulties which can arise when they are implemented in the finite-precision arithmetic of digital computers. The rounding errors which then result can cause many of these algorithms to produce catastrophically bad results, particularly if the initial data supplied is poorly scaled. The numerical analysis background required to study these problems is given in the paper, and methods available to overcome them described. These are detailed with special reference to the SLICE library of numerically reliable Fortran algorithms for control.