Controllability and Observability of Linear Quaternion-valued Systems |
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| Authors: | Bang Xin JIANG Yang LIU Kit Ian KOU Zhen WANG |
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| Institution: | 1.College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, P. R. China;2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, P. R. China;3.College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China |
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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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| Keywords: | Linear system controllability observability quaternion |
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