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

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

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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.

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 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 93 Systems theory; control
Depositing User:	Nick Higham
Date Deposited:	26 Mar 2008
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1062

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