Title :
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
fDate :
12/1/1993 12:00:00 AM
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;
Journal_Title :
Control Systems Technology, IEEE Transactions on