Computing different realizations of linear dynamical systems with embedding eigenvalue assignment

Szlobodnyik Gergely and Szederkényi Gábor: Computing different realizations of linear dynamical systems with embedding eigenvalue assignment. In: Acta cybernetica, (25) 3. pp. 585-611. (2022)

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In this paper we investigate realizability of discrete time linear dynamical systems (LDSs) in fixed state space dimension. We examine whether there exist different Θ = (A,B,C,D) state space realizations of a given Markov parameter sequence Y with fixed B, C and D state space realization matrices. Full observation is assumed in terms of the invertibility of output mapping matrix C. We prove that the set of feasible state transition matrices associated to a Markov parameter sequence Y is convex, provided that the state space realization matrices B, C and D are known and fixed. Under the same conditions we also show that the set of feasible Metzler-type state transition matrices forms a convex subset. Regarding the set of Metzler-type state transition matrices we prove the existence of a structurally unique realization having maximal number of non-zero off-diagonal entries. Using an eigenvalue assignment procedure we propose linear programming based algorithms capable of computing different state space realizations. By using the convexity of the feasible set of Metzler-type state transition matrices and results from the theory of non-negative polynomial systems, we provide algorithms to determine structurally different realization. Computational examples are provided to illustrate structural non-uniqueness of network-based LDSs.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2022
Volume: 25
Number: 3
ISSN: 0324-721X
Page Range: pp. 585-611
Language: English
Publisher: University of Szeged, Institute of Informatics
Place of Publication: Szeged
Event Title: Conference of PhD Students in Computer Science (12.) (2020) (Szeged)
Related URLs:
DOI: 10.14232/actacyb.291870
Uncontrolled Keywords: Számítástechnika, Programozás, Algoritmus
Additional Information: Bibliogr.: p. 606-609. ; ill. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2022. May. 13. 09:29
Last Modified: 2022. May. 13. 09:29

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