Observers for systems characterized by semigroups

The theory of observers is generalized from finite dimensional linear systems to abstract linear systems characterized by semigroups on Banach spaces. Sufficient conditions are given for both identity and reduced-order observers to exist for the abstract system. It is shown that the spectrum of a closed-loop control system using an observer is the union of the spectrum of the observer and the spectrum of the closed-loop system with state feedback. The observer theory for the abstract system is used to show that observability is a sufficient condition for the existence of an observer for a system modeled by a linear functional differential equation.