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2008.35: Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems

2008.35: Ralph Byers, D. Steven Mackey, Volker Mehrmann and Hongguo Xu (2008) Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems.

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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.

Item Type:MIMS Preprint
Additional Information:

Appears also as Preprint 2008-14, Institut fur Mathematik, Technische Universitat Berlin, Germany, March 2008

Uncontrolled Keywords: discrete-time linear-quadratic control, symplectic matrix, symplectic pencil, BVD-pencil, BVD-polynomial, palindromic pencil, palindromic matrix polynomial
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MSC 2000 > 93 Systems theory; control
MIMS number:2008.35
Deposited By:Nick Higham
Deposited On:26 March 2008

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