Identifiability analysis of linear time-delay systems

Identifiability analysis is developed for linear time-delay systems with delayed states, control inputs and measured outputs, all with a finite number of lumped delays. These systems are governed by linear functional differential equations with uncertain time-invariant parameters and delays. It is shown that the transfer function of such a system admits the online identification if a sufficiently nonsmooth input signal is applied to the system. Sufficiently nonsmooth signals are constructively defined by imposing different smoothness properties on the control input and the state of the system. This definition is verified independently of any underlying time-delay system. By applying the theory developed to linear time-delay systems whose states are available to measurements with an a priori known sensor delay, the system parameters and delays are proven to be, in principle, identifiable if and only if the system is weakly controllable. Just in case, the parameter identifiability is also enforced by a sufficiently nonsmooth control input