On the observability and detectability of non-commensurate time-delay linear systems

We tackle the observability and detectability problems of a sort of non-commensurate time-delayed linear systems. We give some conditions under which the system can be put into an observability form, that is the system is decomposed into what we call its observable and unobservable parts. Based on concrete definitions of observability and detectability, we use the observability form to derive observability and detectability conditions.