Rate-limiter stability analysis comparing bifurcation and LMI-based approaches

Author

Bombieri, Eduardo ; Pagano, Daniel J. ; Ponce, Enrique

Author_Institution

Dept. of Autom. & Syst., Fed. Univ. of Santa Catarina, Florianopolis, Brazil

fYear

2011

fDate

19-21 Dec. 2011

Firstpage

1168

Lastpage

1173

Abstract

The effect of rate-limiters in open loop unstable systems is studied. First order plants with a rate-limiter in the feedback loop are considered, leading to discontinuous second order differential systems. Two different analysis methods are applied. Firstly, through bifurcation analysis, the existence of a unstable limit cycle is proved and expressions for its size and period are provided. Next, a linear matrix inequalities based analysis is carried out and an ellipsoidal approximation of the basin of attraction is obtained. Finally, the advantages and disadvantages of each approach are highlighted.

Keywords

linear matrix inequalities; open loop systems; stability; LMI based approaches; discontinuous second order differential systems; ellipsoidal approximation; feedback loop; linear matrix inequalities; open loop unstable systems; rate limiter stability analysis comparing bifurcation; Bifurcation; Closed loop systems; Ellipsoids; Feedback loop; Limit-cycles; Mathematical model; Stability analysis; Bifurcations; Limit cycles; Linear Matrix Inequalities (LMIs); Rate-Limiters;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Automation (ICCA), 2011 9th IEEE International Conference on

Conference_Location

Santiago

ISSN

1948-3449

Print_ISBN

978-1-4577-1475-7

Type

conf

DOI

10.1109/ICCA.2011.6137893

Filename

6137893