Abstract
This paper considers the design problem of an observer to estimate a linear function of the state variables of a linear system, used in implementing a feedback control law.
Conditions of linear functions for the existence of an observer of a given order are obtained both in the case that the observer has only a specified pole configuration and in the case that it can have an arbitrary pole configuration. When a linear function and a pole configuration satisfying the conditions are given, a construction of the observer estimating the linear function and having the pole configuration is shown.
A loss of a performance index caused by using an observer for implementing the optimal feedback control law in the optimal regulator problem is discussed, and it is shown that if the loss can be made arbitrarily small by using and choosing an observer estimating all state variables, then it is the case with using an observer only estimating the linear feedback function and choosing the poles of the observer.
