DECOMPOSABILITY AND QUOTIENT SUBSPACES FOR THE PENCIL SL-M

This paper introduces the notion of decomposability of the domain and the codomain relative to the generalized nonsquare matrix pencil PI(s) = sL - M. Its importance is justified rigorously and it is demonstrat ed that a special case of these new results is the familiar notion of decomposability for the pencil sI - M. This definition is motivated by the concepts of strict equivalence and quotient subspaces. By decompo sing both the domain and the codomain of L and M the close relation be tween decomposability and the Kronecker invariants of the pencil sL - M is shown. Finally, an application of the notion of decomposabilty in controls design is presented.