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Strong Structural Properties of Structured Linear Systems

Shali, Brayan (2019) Strong Structural Properties of Structured Linear Systems. Master's Thesis / Essay, Applied Mathematics.

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Abstract

This master thesis deals with structured systems and their strong structural properties. The structured systems studied in this thesis describe a family of linear systems in which the entries of the system matrices are fixed zeros, nonzeros or arbitrary real numbers. The definition of a structured system is formalized with the help of pattern matrices, and strong structural properties are characterized as rank properties of these pattern matrices. In parallel to these algebraic characterizations, we provide equivalent graph-theoretic characterizations based on the so-called system graph. In particular, we provide a sufficient condition for strong structural output controllability, necessary and sufficient conditions for strong structural input-state observability, and three mutually unrelated sufficient conditions for strong structural left invertibility. We also discuss the limitations of the approach taken in this thesis, which are most evident in the search for necessary conditions for strong structural output controllability and left invertibility. Finally, we extend the already existing necessary and sufficient conditions for strong structural controllability of linear systems to linear descriptor systems.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor:
Supervisor nameSupervisor E mail
Camlibel, M.K.M.K.Camlibel@rug.nl
Trentelman, H.L.H.L.Trentelman@rug.nl
Degree programme: Applied Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 29 Aug 2019
Last Modified: 29 Aug 2019 14:47
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/20833

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