A geometric approach to the classification of singular systems

The author considers the singular system Ex´(t) =Ax(t)+Bu(t) where E,A :X→Y and B:U→Y are linear maps. It is assumed that X=Rⁿ , Y=R^P and U=R^m and therefore no assumptions such as regularity, regularizability, etc. are made about the system under consideration. The author presents direct-sum decompositions of X and Y which immediately induce a canonical form of (E ,A,B) under the action of the generalized Brunovsky group. A complete orbital invariant for this action is defined using geometric algorithms