Robust stability analysis using the small gain, circle, positivity, and Popov theorems: a comparative study

Author

Haddad, Wassim M. ; Collins, Emmanuel G., Jr. ; Bernstein, D.S.

Author_Institution

Dept. of Mech. & Aerosp. Eng., Florida Inst. of Technol., Melbourne, FL, USA

Volume

1

Issue

4

fYear

1993

fDate

12/1/1993 12:00:00 AM

Firstpage

290

Lastpage

293

Abstract

The stability robustness of a maximum-entropy controller designed for a benchmark problem is examined. Four robustness tests are used, i.e., small gain analysis, circle analysis, positive real analysis, and Popov analysis, each of which is guaranteed to give a less conservative result than the previous test. The analysis is performed graphically. The Popov test is seen, for this example, to yield highly nonconservative robust stability bounds. The results illuminate the conservatism of analysis based on traditional small-gain type tests and reveal the effectiveness of analysis tests based on Popov analysis and related parameter-dependent Lyapunov functions

Keywords

Popov criterion; control system analysis; stability; Popov theorem; benchmark problem; circle theorem; graphical analysis; highly nonconservative robust stability bounds; maximum-entropy controller; parameter-dependent Lyapunov functions; positive real analysis; positivity theorem; robust stability analysis; small gain theorem; Feedback; Lyapunov method; Performance analysis; Robust control; Robust stability; Robustness; Stability analysis; State-space methods; Testing; Uncertainty;

fLanguage

English

Journal_Title

Control Systems Technology, IEEE Transactions on

Publisher

ieee

ISSN

1063-6536

Type

jour

DOI

10.1109/87.260275

Filename

260275