https://www.math.bgu.ac.il/~paf/symmetric.pdf

On symmetric rational transfer functions

Duality is studied in the context of polynomial models for linear systems. The output injection group, the dual of the feedback group, is studied and a polynomial characterization of ( C, A )-invariant subspaces as well as of the maximal reachability subspaces contained in ker C is given.

/pdf/duality-in-polynomial-models-with-some-applications-to-4sttxwkwpl.pdf

Duality in polynomial models with some applications to geometric control theory

A unifying approach to the decoupling problem (diagonal, triangular, block decoupling) is introduced. The key element is the interactor, a polynomial matrix of unique structure associated with the transfer matrix of the system. Necessary and sufficient conditions for block decoupling are derived and the stability questions are resolved using the block coupling zeros. The results obtained (for decoupling via state feedback, state feedback plus input dynamics and constant output feedback) are conceptually simple, unify and expand those existing, and easily lead to constructive decoupling algorithms.

A unifying approach to the decoupling of linear multivariate systems

Smith-McMillan factorizations at infinity of rational matrix functions and their control interpretation

This paper describes an application of the theory of polynomial models to the study of some natural objects in geometric control theory. In particular, it utilizes the correspondence between factorization of polynomial matrices and invariant subspaces to obtain, by the use of Toeplitz operators, a polynomial characterization of (A, B) invariant subspaces as well as those included in her C. A geometric characterization of feedback irreducibility is rederived.

J.C. Willems

Papers

Factorization indices at infinity for rational matrix functions : (preprint)