Laplace and Cayley transforms -an approximation point of view

We interpret the Cayley transform of linear (finite-or infinite-dimensional) state space systems as a numerical integration scheme of Crank–Nicolson type. If such a scheme is applied to a conservative system, then the resulting discrete time system is conservative in the discrete time sense. We show that the convergence of this integration scheme is equivalent to an approximation of the Laplace transform.