Controllability and Observability of Linear Quaternion-valued Systems

被引：16
|
作者：
Jiang, Bang Xin [1 ]
Liu, Yang [1 ]
Kou, Kit Ian [2 ]
Wang, Zhen [3 ]
机构：
[1] Zhejiang Normal Univ, Coll Math Phys & Informat Engn, Jinhua 321004, Zhejiang, Peoples R China
[2] Univ Macau, Fac Sci & Technol, Dept Math, Macau, Peoples R China
[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2020年 / 36卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Linear system; controllability; observability; quaternion; NEURAL-NETWORKS; STATE; STABILIZATION; EQUATIONS;
D O I：
10.1007/s10114-020-8167-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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-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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页码：1299 / 1314
页数：16
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