Controllability and Observability of Linear Quaternion-valued Systems

The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or c...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 36; no. 11; pp. 1299 - 1314
Main Authors Jiang, Bang Xin, Liu, Yang, Kou, Kit Ian, Wang, Zhen
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2020
Springer Nature B.V
Subjects
Controllability
Duality theorem
Linear systems
Mathematics
Mathematics and Statistics
Observability (systems)
Quaternions
Stability
Linear system
controllability
quaternion
93B07
93C05
93B05
34A30
observability
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Summary:The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-020-8167-1