Abstract
Pole locations of LQ regulators for a dynamical system (D.S.) and its augmented state system (A.D.S.) are discussed. The A.D.S. considered is made by adding to the state variable the integral z of the output y of the original D.S. The performance index of the A.D.S. is made by adding to the integrand of the original performance index a quadratic form ε2z'Q2z. Poles of the LQ regulator for the A.D.S. can be divided into two classes. Any pole of the first class is shown to lie near a pole of the LQ regulator of D.S. with distance of O(ε2).
Poles of the second class can be approximated by ε/κ. Here, κ's are real and negative, and are given by square roots of principal values of a certain regular pencil. Therefore, it may be said that poles of the first class are not so much affected as those of the second class when ε varies. By using above mentioned properties of the pole location, a method is proposed to choose the quadratic weight to the z part of the state of A.D.S.
