Controllability and Observability of Linear Quaternion-valued Systems

被引：0
作者：
Bang Xin Jiang
Yang Liu
Kit Ian Kou
Zhen Wang
机构：
[1] Zhejiang Normal University,College of Mathematics, Physics and Information Engineering
[2] University of Macau,Department of Mathematics, Faculty of Science and Technology
[3] Shandong University of Science and Technology,College of Mathematics and Systems Science
来源：
Acta Mathematica Sinica, English Series | 2020年 / 36卷
关键词：
Linear system; controllability; observability; quaternion; 34A30; 93B05; 93B07; 93C05;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：1299 / 1314
页数：15
相关论文
共 81 条
[1]  
Chen X(2017)State estimation for quaternion-valued neural networks with multiple time delays IEEE Transactions on Systems, Man, and Cybernetics: Systems 49 2278-2287
[2]  
Song Q(2017)Design and analysis of quaternion-valued neural networks for associative memories IEEE Transactions on Systems, Man, and Cybernetics: Systems 48 2305-2314
[3]  
Chen X(2017)Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons IEEE Transactions on Neural Networks and Learning Systems 29 2769-2781
[4]  
Song Q(2018)A unified analysis of linear quaternion dynamic equations on time scales Journal of Applied Analysis and Computation 8 172-201
[5]  
Li Z(2020)Floquet theory for quaternion-valued differential equations Qualitative Theory of Dynamical Systems 19 3-45
[6]  
Chen X(2003)Solving simple quaternionic differential equations Journal of Mathematical Physics 44 2224-2233
[7]  
Song Q(2014)Convergence in Acta Mathematica Sinica, English Series 30 1566-1578
[8]  
Li Z(1847)-norm of Fourier series on the complete product of quaternion groups with bounded orders Proc. Roy. Irish Acad. 3 441-448
[9]  
Cheng D(1844)On the application of the method of quaternions to some dynamical questions Proc. Roy. Irish Acad. 2 424-434
[10]  
Kou K I(1970)On a new species of imaginary quantities connected with a theory of quaternions Indagationes Mathematicae (Proceedings) 73 448-455
123456789