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Controllability of Linear Structured Systems on Colored Pattern Matrices

Charalampidis, Nikolaos (2019) Controllability of Linear Structured Systems on Colored Pattern Matrices. Master's Thesis / Essay, Applied Mathematics.


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In this thesis, strong structural controllability of linear structured systems on zero/nonzero/arbitrary pattern matrices is studied. In the research on strong structural controllability, a key assumption is that the nonzero entries are independent in given pattern matrices. However, this is not always satisfied in many physical or mechanical systems. In particular, some nonzero entries in the system matrices are constrained to take identical values. In order to represent such systems, we introduce the concepts of colored pattern matrices and colored structured systems. We then establish sufficient algebraic conditions for controllability of colored structured systems in terms of full row rank tests on two associated colored pattern matrices. In addition, we test the necessity of our conditions for three special cases of colored structured systems. Furthermore, we establish a necessary and sufficient graph theoretic test for the nonsingularity of a square colored pattern matrix in which the entries are allowed to be complex values. Upon this result, for a colored graph associated with a given colored pattern matrix, we introduce the notions of color perfect neighbors, color change rules and colorability which results in a graph theoretic test for full rank property of such colored pattern matrices. Combing the previous algebraic conditions, we develop graph theoretic conditions for controllability of colored structured systems. In addition, we compare our results to those in the existing literature and explain what is generalized by our framework. Finally, we extend our results to structured systems on colored pattern matrices with an additional constraint.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor nameSupervisor E mail
Degree programme: Applied Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 07 Jul 2019
Last Modified: 11 Jul 2019 12:53

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