caa a22 4500 445868635 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00498-011-0059-6 doi (NATIONALLICENCE)springer-10.1007/s00498-011-0059-6 A permuted factors approach for the linearization of polynomial matrices [Elektronische Daten] [S. Vologiannidis, E. Antoniou] In Antoniou and Vologiannidis (Electron J Linear Algebra 11:78-87, 2004; 15:107-114, 2006), a new family of companion forms associated with a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in Fiedler (Linear Algebra Its Appl 371:325-331, 2003) where the scalar case was considered. In this paper, extending this "permuted factors” approach, we present a broader family of companion-like linearizations, using products of up to n(n−1)/2 elementary matrices, where n is the degree of the polynomial matrix. Under given conditions, the proposed linearizations can be shown to consist of block entries where the coefficients of the polynomial matrix appear intact. Additionally, we provide a criterion for those linearizations to be block symmetric. We also illustrate several new block symmetric linearizations of the original polynomial matrix T (s), where in some of them the constraint of nonsingularity of the constant term and the coefficient of maximum degree are not a prerequisite. Springer-Verlag London Limited, 2011 Polynomial matrices nationallicence Linearizations nationallicence Realizations nationallicence Companion matrix nationallicence Linear systems nationallicence Vologiannidis S. Department of Mathematics, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece aut Antoniou E. Department of Sciences, Technological Educational Institute of Thessaloniki, 57400, Sindos, Greece aut Mathematics of Control, Signals, and Systems Springer-Verlag 22/4(2011-08-01), 317-342 0932-4194 22:4<317 2011 22 498 https://doi.org/10.1007/s00498-011-0059-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00498-011-0059-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vologiannidis S. Department of Mathematics, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece aut NATIONALLICENCE 700 1- Antoniou E. Department of Sciences, Technological Educational Institute of Thessaloniki, 57400, Sindos, Greece aut NATIONALLICENCE 773 0- Mathematics of Control, Signals, and Systems Springer-Verlag 22/4(2011-08-01), 317-342 0932-4194 22:4<317 2011 22 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer