Observers for Linear Time-Delay Systems

Abstract

This paper is concerned with the deterministic state estimation problem for a linear time-invariant system with delay
x(t)=Ax(t)+Dx(t-h)+Bu(t), h>0
y(t)=Cx(t).
The object is to find a sufficient condition for the constructibility of an observer which yields an estimate that approaches x(t) as t→∞.
The result is as follows. If (i) (C, A) is an observable pair, and (ii) when (C, A) is written in a Luenberger's canonical form, D=D₁+D₂ where D₁ is a matrix having rows written as linear combinations of the rows of C, and D₂ is an upper triangular matrix, then an observer is constructible under an arbitrary specification of the degree of the decay of the estimation error.