Extreme point results for robust stabilization of interval plants with first-order compensators

Author

Barmish, B. Ross ; Hollot, Christopher V. ; Kraus, Frank J. ; Tempo, Roberto

Author_Institution

Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA

Volume

37

Issue

6

fYear

1992

fDate

6/1/1992 12:00:00 AM

Firstpage

707

Lastpage

714

Abstract

It has been shown previously that a first-order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants. These extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients. In this work, the authors prove a stronger result, namely, that it is necessary and sufficient to stabilize only sixteen of the extreme plants. These sixteen plants are generated using the Kharitonov polynomials associated with the numerator and denominator. Furthermore, when additional information about the compensator is specified (sign of the gain and signs and relative magnitudes of the pole and zero), then, in some cases, it is necessary and sufficient to stabilize eight critical plants, while, in other cases, it is necessary and sufficient to stabilize twelve critical plants

Keywords

compensation; polynomials; stability; Kharitonov polynomials; critical plants; first-order compensators; interval plants; robust stabilization; Automatic control; Feedback control; Helium; Industrial electronics; Poles and zeros; Polynomials; Robust stability; Robustness; Uncertainty;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.256326

Filename

256326