Design of low-order observers for linear feedback control laws

Abstract

This paper considers the problem of designing an observer to estimate a linear function of the state of a linear system, for the purpose of implementing a feedback control law. In the single-output case a necessary and sufficient condition is found for the existence of an observer of given order and pole configuration. A procedure is stated for constructing the observer, and an algorithm for determining minimal order is outlined. The multi-output case is reduced via a canonical form to an output-coupled set of single-output systems which can be treated as above. Observers derived using these procedures are generally of lower order than those of Luenberger, and the restriction that plant and observer have no common poles is unnecessary.