Relative Controllability of Linear Quaternion Discrete System With Delay

• 成果类型: Article
• 署名作者: Wang, JinRong; Chen, Dan
• 署名单位: Guizhou University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3578503
• 发表日期: 2025
• 关键词: differential-equations; REPRESENTATION

摘要

The linear quaternion discrete system (LQDS) serves as an effective mathematical tool for applications in wave modeling, fluid dynamics, and filter design. This article is dedicated to the analysis of relative controllability for LQDS with delay. Formulas for the exact solutions of system trajectories are derived by using a delay-adapted quaternion discrete matrix exponential. The Gram and rank criteria for the relative controllability of LQDS with pure delay are established by the quaternion delayed Gram matrix and the division ring of reachability for quaternions, respectively. A necessary and sufficient condition is provided to ensure that LQDS with delay and nonpermutable matrices is relatively controllable. Furthermore, an appropriate control function is constructed to solve the problem of relative controllability. The results are illustrated by an example.