  One of the most interesting questions in control theory is that of
constructing observers. Observers compute estimates of the internal states of a
dynamical system, using data provided by measurement probes or partial state
information. For linear systems, Luenberger observers (also known as
"deterministic Kalman filters" since they amount to Kalman filters designed
without regard to the statistics of measurement noise) provide a general
solution, but, for nonlinear systems, establishing generally applicable
conditions for existence and convergence of observers is an open and active
area of research. This paper provides a necessary and sufficient condition for
detectability, and an explicit construction of observers when this condition is
satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero
deficiency type.
