Two-dimensional descriptor systems

Linear descriptor systems are governed by dynamical equations subject to algebraic constraints. In the one-dimensional case, where only depend on a single index, usually time, Weierstrass canonical form splits up state vector in two parts, causal part, running forward and non-causal backward. this paper linear time-invariant autonomous two-dimensions discussed condition existence of non-trivial solution is derived, together with an explicit formula for output such systems. It shown that model can be related part each dimensions model, backward various respectively. The results obtained requiring solutions, states outputs, which defined two-dimensional grid, path invariant unique.