Construction of Observers for a Delay Differential System with One-Dimensional Output

Abstract

We construct systems for estimating the solutions of a spectrally observable linear autonomous system with commensurable delays from the one-dimensional output with various dynamic properties: (i) the estimation error is the output of an asymptotically stable system of the same type (an asymptotic observer); (ii) starting from some time, the output of the observer system is identically equal to the solution of the original system (a finite observer), and simultaneously, the observer is asymptotic (a complete observer). The results are illustrated with examples.