Investigation of controllability and observability for linear quaternion-valued systems from its complex-valued systems (Q2143191)

The authors of this paper used a novel method to examine the controllability and observability of linear quaternion-valued systems (QVS) from the perspective of complex-valued systems, and they established an equivalence between the complete controllability of linear QVS and its complex-valued system. Furthermore, two efficient criteria for the linear QVS's controllability and observability in the sense of complex representation were defined. The authors also offered a straightforward approach to solving the control function. In order to demonstrate the theoretical results, utilise numerical examples.