Complete controllability conditions for linear time-independent system with delay in output

Strict justification and extension to the linear stationary system with delay in the equation of state and in the output of one approach to reception of complete observability conditions for systems with delay is executed. The approach is based on the reduction of the problem of complete observability of the system with delay to the problem of uniqueness of the solution of a special homogeneous boundary value problem for a system of differential equations without delay in the extended state space. The necessary and sufficient conditions for complete observability, complete identifiability are proved. Complete observability, identifiability in the sense of unambiguous reconstruction of an unobservable piece of the trajectory on the time period of the delay length by the known output function are proved. The conditions are of rank type and are expressed in terms of matrices of the original observation system.