Observability and Geometric Approach of 2D Hybrid Systems

A connection is emphasized between two branches of the Systems Theory, namely the Geometric Approach and 2D Systems, with a special regard to the concept of observability. An algorithm is provided which determines the maximal subspace which is invariant with respect to two commutative matrices and which is included in a given subspace. Observability criteria are obtained for a class of 2D systems by using a suitable 2D observability Gramian and some such criteria are derived for LTI 2D systems, as well as the geometric characterization of the subspace of unobservable states. The presented algorithm is applied to determine this subspace.