This paper discusses the problem of designing a single linear functional observer (S. L. F. O.) to estimate a single linear function of the state of a linear time-invariant system, for the purpose of implementing a feedback control law.
First, canonical forms of S. L. F. O. are obtained both in the case that S. L. F. O. can have arbitrary poles and in the case that poles of S. L. F. O. must satisfy a constraint condition. Second, an algorithm obtaining the optimal S. L. F. O. is easily derived by using this canonical form. The optimal criterion is the time-integral of the mean-square estimation error. By the presented procedure, the S. L. F. O. is designed under the following conditions:
(1) poles of S. L. F. O. have the most possible freedom of choice,
(2) the order of S. L. F. O. is as small as possible,
(3) the number of paths of S. L. F. O. is as few as possible,
(4) optimality.
Finally, an illustrative example for a power system is given to show the effectiveness of the presented method.
