Minimal order observers for estimating linear functions of a state vector

This paper studies the necessary and sufficient conditions for a pth-order observer to observe linear functions of the states of a linear dynamical system. The conditions are a set of multivariable polynomial equations which must be satisfied for some variable set in order for a pth-ncder observer to exist. It is possible to test for the existence of such a variable set in a finite number of steps via decision methods and thereby to construct an observer with the aid of polynomial factorization. To minimize the computational effort, the necessary and sufficient conditions are expressed in terms of the minimum number of variables.