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