  This work builds on an existing model of discrete canonical evolution and
applies it to the general case of a linear dynamical system, i.e., a
finite-dimensional system with configuration space isomorphic to $
\mathbb{R}^{q} $ and linear equations of motion. The system is assumed to
evolve in discrete time steps. The most distinctive feature of the model is
that the equations of motion can be irregular. After an analysis of the arising
constraints and the symplectic form, we introduce adjusted coordinates on the
phase space which uncover its internal structure and result in a trivial form
of the Hamiltonian evolution map. For illustration, the formalism is applied to
the example of massless scalar field on a two-dimensional spacetime lattice.
