Structural invariants of implicit two-dimensional systems

Fundamental structural properties are identified for a class of implicit two-dimensional (2-D) system models with a form that is closed under static local-state feedback and output-injection transformations. The structural properties are investigated in terms of quater-plane causal solutions given compatible boundary conditions, controlled and conditioned invariants, and the corresponding output-nulling and input-containing subspaces. As is well known, such concepts play an important role in systems theory and in the solution of several control and estimation problems.