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Preprint 14-2008

Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems

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Author(s) : Ralph Byers , D. Steven Mackey , Volker Mehrmann , Hongguo Xu

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 14-2008

MSC 2000

65F15 Eigenvalues, eigenvectors
15A21 Canonical forms, reductions, classification

Abstract :
We give several different formulations for the discrete-time linear-quadratic control problem in terms of structured eigenvalue problems, and discuss the relationships among the associated structured objects: symplectic matrices and pencils, BVD-pencils and polynomials, and the recently introduced classes of palindromic pencils and matrix polynomials. We show how these structured objects can be transformed into each other, and also how their eigenvalues, eigenvectors and invariant/deflating subspaces are related.

Keywords : discrete-time linear-quadratic control, symplectic matrix, symplectic pencil, BVD-pencil, BVD-polynomial, palindromic pencil, palindromic matrix polynomial

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