Polynomial characterizations of (H,F)-invariant subspaces with applications (Q1079629)

Let Z be a \(p\times m\) strictly proper transfer matrix in polynomial fractional representation \(Z=PQ^{-1}R+W\). The author obtains polynomial characterizations for (H,F)-invariant subspaces associated with the realization \(\Sigma (P,Q,R,W)=(F,G,H,X_ Q)\) [cf. \textit{P. Fuhrmann}, J. Franklin Inst. 301, 521-540 (1976; Zbl 0332.93001)]. For full rank transfer matrices, he describes in terms of factors of the polynomial system matrix the smallest unobservability subspace containing Im G and largest reachability subspace in Ker H. Moreover he applies the obtained results to the stabilization problem with measurement feedback and to the disturbance decoupling problem with measurement feedback. In both cases he first gives the polynomial solvability conditions and, with the help of the characterizations developed for (H,F)-invariant subspaces obtains geometric interpretations.