Identifiability of delayed singular systems

In this paper we derive a condition for delayed singular system to be identified with input-state data. Identifiability condition is given for a singular system with input delays. Dynamics of singular systems can be seen as a combination of dynamics from regular system and nilpotent system, i.e., coefficient matrix of differentiation of state is nilpotent matrix. Dynamics of nilpotent system is well analyzed in terms of distribution theory. Therefore identifiability property of singular system is well-analyzed in terms of distribution theory. We show that identifiability of delayed singular system is related with weak S controllability.