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Controllability and Observability of Linear Quaternion-valued Systems

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Abstract

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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Acknowledgements

We thank the referees for their time and comments.

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Correspondence to Kit Ian Kou.

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Supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. LR20F030001 and LD19A010001), by the National Natural Science Foundation of China (Grant No. 11671361), by the University of Macau (Grant No. MYRG2019-00039-FST), and by the Science and Technology Development Fund, Macau SAR (Grant No. FDCT/085/2018/A2)

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Jiang, B.X., Liu, Y., Kou, K.I. et al. Controllability and Observability of Linear Quaternion-valued Systems. Acta. Math. Sin.-English Ser. 36, 1299–1314 (2020). https://doi.org/10.1007/s10114-020-8167-1

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  • DOI: https://doi.org/10.1007/s10114-020-8167-1

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