caa a22 4500 445868643 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00498-011-0061-z doi (NATIONALLICENCE)springer-10.1007/s00498-011-0061-z Equivalence conditions for behaviors and the Kronecker canonical form [Elektronische Daten] [P. Fuhrmann, U. Helmke] In this paper we explore equivalence conditions and invariants for behaviors given in kernel representations. In case the kernel representation is given in terms of a linear matrix pencil, the invariants for strict equivalence are given by the Kronecker canonical form which, in turn, we interpret in geometric control terms. If the behavior is given in a kernel representation by a higher order rectangular polynomial matrix, the natural equivalence concept is behavior equivalence. These notions are closely related to the Morse group that incorporates state space similarity transformations, state feedback, and output injection. A simple canonical form for behavioral equivalence is given that clearly exhibits the reachable and autonomous parts of the behavior. Using polynomial models we also present a unified approach to pencil equivalence that elucidates the close connections between classification problems from linear algebra, geometric control theory, and behavior theory. We also indicate how to derive the invariants under behavior equivalence from the Kronecker invariants. Springer-Verlag London Limited, 2011 Kronecker canonical form nationallicence Behaviors nationallicence Strict equivalence nationallicence Matrix pencils nationallicence Fuhrmann P. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel aut Helmke U. Institut für Mathematik, Universität Würzburg, Würzburg, Germany aut Mathematics of Control, Signals, and Systems Springer-Verlag 22/4(2011-08-01), 267-293 0932-4194 22:4<267 2011 22 498 https://doi.org/10.1007/s00498-011-0061-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00498-011-0061-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fuhrmann P. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel aut NATIONALLICENCE 700 1- Helmke U. Institut für Mathematik, Universität Würzburg, Würzburg, Germany aut NATIONALLICENCE 773 0- Mathematics of Control, Signals, and Systems Springer-Verlag 22/4(2011-08-01), 267-293 0932-4194 22:4<267 2011 22 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer