Controllability and Observability of Linear Quaternion-valued Systems

被引：17

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.

引用

页码：1299 / 1314

页数：16