About the exact determination of the solution to linear completely regular differential-algebraic systems with delay

We study the problem of exact reconstruction of the solution from measurements of the observed output for linear autonomous completely regular differential-algebraic systems with commensurate delays. The reconstruction process is implemented using a finite observer, which is the output of a linear autonomous retarded system type with commensurate concentrated and distributed delays and a predetermined finite spectrum. The criterion for the existence of such an observer is obtained.