Global temporal observability of linear dynamic systems

In this paper, we introduce a new concept termed global temporal observability for continuous and discrete linear dynamic systems and explore its connection with the classical notion of observability. It is shown that, as a concept, global temporal observability is a generalization of the classical observability. However, as a feature of a dynamic system, global temporal observability is embedded into classical observability. The necessary condition for global temporal observability is presented. Four linear systems were considered to test the proposed concept. Since observability is a binary test, our results matched the results of classical observability analysis when appropriate basis functions are utilized. The advantages and disadvantages of the proposed concept are discussed. The main advantage of global temporal observability is that it restores the state function for the entire time duration in a single step that requires matrix inversion. It is shown that global temporal observability connects state reconstruction, differential equations, and observability concepts.