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Investigation of Controllability and Observability for Linear Quaternion-Valued Systems from Its Complex-Valued Systems

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Abstract

In this paper, we adopt a new approach to study the controllability and observability of linear quaternion-valued systems (QVS) from the point of complex-valued systems, which is much different from the method used in the previous paper. We show the equivalence relation of complete controllability for linear QVS and its complex-valued system. Then we establish two effective criteria for controllability and observability of the linear QVS in the sense of complex representation. In addition, we give a direct method to solve the control function. Finally, we use numerical examples to illustrate our theoretical results.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Dan Chen & JinRong Wang

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

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  1. Dan Chen
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  2. Michal Fečkan
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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.

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Chen, D., Fečkan, M. & Wang, J. Investigation of Controllability and Observability for Linear Quaternion-Valued Systems from Its Complex-Valued Systems. Qual. Theory Dyn. Syst. 21, 66 (2022). https://doi.org/10.1007/s12346-022-00599-6

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  • DOI: https://doi.org/10.1007/s12346-022-00599-6

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