Byers, RalphMackey, D. StevenMehrmann, VolkerXu, Hongguo2021-12-172021-12-172008-03-122197-8085https://depositonce.tu-berlin.de/handle/11303/15646http://dx.doi.org/10.14279/depositonce-14419We 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.en510 Mathematikdiscrete-time linear-quadratic controlsymplectic matrixsymplectic pencilBVD-pencilBVD-polynomialpalindromic pencilpalindromic matrix polynomialResearch Paper