The Cayley Transform as a Time Discretization Scheme

We interpret the Cayley transform of linear (finiteor infinite-dimensional) state space systems as a numerical integration scheme of Crank–Nicolson type. The scheme is known as Tustin’s method in the engineering literature, and it has the following important Hamiltonian integrator property: if Tustin’s method is applied to a conservative (continuous time) linear system, then the resulting (discrete time) linear system is conservative in the discrete time sense. The purpose of this paper is to study the convergence of this integration scheme from the input/output point of view.