Decomposability and Quotient Subspaces for the Pencil $sL - M$
Vassilis L. Syrmos, Frank L. Lewis · SIAM Journal on Matrix Analysis and Applications · 1994
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 demonstrated 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 decomposing both the domain and the codomain of L and M the close relation between 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.