Duality in time-varying linear systems: A module theoretic approach
type: Item
instance of: scholarly article
title: Duality in time-varying linear systems: A module theoretic approach
zbMATH Open document ID: 0864.93035
DOI: 10.1016/0024-3795(94)00222-3
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 1997-06-15T00:00:00Z
review text: This paper endeavours to give a more satisfactory treatment to the question of systems duality for time-varying linear systems than the general procedure of transposing matrices and changing signs. The authors use the module theoretic approach introduced by \textit{M. Fliess} [Syst. Control Lett. 15, No. 5, 391-396 (1990; Zbl 0727.93024)], where a left module represents the system, to define the dual system as the corresponding right module. Using this definition, the duality between controllability and observability as well as between state feedback and output injection are subsequently established. The Brunovsky form, an important canonical form for linear systems under static state feedback, is shown to be a canonical form for controllable linear time-varying systems under quasistatic state feedback as well. The dual result is also given. It is shown that the classical observability indices can be introduced by using filtrations and the classical controllability indices may then be defined by duality. Two examples complete this paper.
reviewed by: Frieda Theron
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93C99
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 931922
zbMATH Keywords: duality
zbMATH Keywords: time-varying
zbMATH Keywords: module
zbMATH Keywords: dual system
zbMATH Keywords: controllability
zbMATH Keywords: observability
zbMATH Keywords: canonical form
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00222-3
OpenAlex ID: W2070777618
cites work: Q5563439
cites work: Algebraic theory for multivariable linear systems
cites work: Q5597890
cites work: Q4108256
cites work: Q3808246
cites work: Variational and Hamiltonian control systems
cites work: Q4014833
cites work: Q4851999
cites work: Generalized linear systems with lumped or distributed parameters and differential vector spaces
cites work: Some basic structural properties of generalized linear systems
cites work: A remark on Willems' trajectory characterization of linear controllability
cites work: Duality in polynomial models with some applications to geometric control theory
cites work: Factorization indices at infinity for rational matrix functions
cites work: Time-varying linear systems and invariants of system equivalence
cites work: Time-varying polynomial matrix systems
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: Q5638871
cites work: Q5680222
cites work: Q5566063
cites work: Differential equations with polynomial coefficients
cites work: Structural Invariants of Linear Multivariable Systems
cites work: Q3830897
cites work: Q4312607
cites work: Q3139478
cites work: Controllability and Observability in Time-Variable Linear Systems
cites work: Paradigms and puzzles in the theory of dynamical systems
cites work: Linear multivariable systems
cites work: Q3975465
cites work: Q3525854
Wikidata QID: Q127488227
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description: scientific article; zbMATH DE number 931922