Relations of Controllability and Observability between Continuous-Time Linear System and Its Projective System

This paper investigates the relations of controllability and observability between continuous-time linear system and its projective system. By using the V-addition, the projective system on a lower dimensional space for continuous-time linear system is obtained. Based on the projective matrix, the relation of controllability between the original continuous-time linear system and its projective system is revealed. Meanwhile, the observability between the original continuous-time linear system and its projective system is also explored. Finally, some numerical examples are presented to illustrate the theoretical results.