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