Digital linear control theory for automatic stepsize control

In transient analysis of electrical circuits the solution is computed by means of numerical integration methods. Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers can ensure that the errors and stepsizes also behave smoothly. For onestep methods, the stepsize control process can be viewed as a digital (i.e. discrete) linear control system for the logarithms of the errors and steps. For the multistep BDF-method this control process can be approximated by such a linear control system.