An observer for linear time-delay systems

In this paper, we propose an observer design for a class of single-output linear systems with known time-delay in the state. First, we introduce a new concept of asymptotic stability for linear time delay systems called the (α, r)-stability. This automatically ensures that the underlying system is stable in the Krasovskii sense which in turn guaranty that the system is asymptotically stable. The observer design is then based on the specific choice of the observer gain such that the corresponding error dynamics is (α, r)-stable. An example is provided to illustrate the design methodology.