Controllability and Observability of Linear Quaternion-valued Systems

• 作者: Bang Xin JIANG Kit Ian KOU Yang LIU Zhen WANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2020,（11）
• 页码范围: 1299-1314
• 页数: 16页
• 语种: 英文

摘要

The aim of this paper is to define an extension of the controllability and observability forlinear 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.