Abstract
Robust stability degree assignment is a method which assigns the poles of the system in a desired region on the complex plane by H∞ control theory. In this paper, the pole location of the nominal system controlled by the central solution is clarified. Namely, it is shown that when the perturbation is additive and the desired region is a half plane to the left of a vertical line s=-α on the complex plane, the poles of the plant and the zeros of the weight inside the desired region do not move, and other poles and zeros are turned over to their mirror images with respect to the vertical line if γ=∞ and some of the poles move if γ becomes smaller.
Since H∞ controller is not usually observer type, the poles cannot be separated into regulator poles and the observer poles. This makes it difficult to clarify the relation between the performance index and the pole location of the closed-loop system in general. The controller designed by the robust stability degree assignment is observer type and the constant terms of Riccati equations are zero. These special properties are used in the proof. The pole location is not clarified for multiplicative perturbation.
