Open AccessImproved Circle and Popov Criteria for systems containing magnitude bounded nonlinearities
Author(s) -
Matthew C. Turner,
Jorge Sofrony
Publication year - 2017
Publication title -
ifac-papersonline
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 72
eISSN - 2405-8971
pISSN - 2405-8963
DOI - 10.1016/j.ifacol.2017.08.1494
Subject(s) - bounded function , magnitude (astronomy) , mathematics , nonlinear system , set (abstract data type) , stability (learning theory) , circle criterion , state (computer science) , control theory (sociology) , marginal stability , mathematical analysis , exponential stability , computer science , algorithm , instability , physics , control (management) , quantum mechanics , astronomy , machine learning , artificial intelligence , mechanics , programming language
This paper presents improved versions of the Circle and Popov Criteria for Lure systems in which the nonlinear element is both sector and magnitude bounded. The main idea is to use the fact that if the nonlinearity is magnitude bounded and the linear system is asymptotically stable, then its state will be ultimately bounded. When the state enters this set of ultimate boundedness, it will satisfy a narrower sector condition which can then be used to prove stability in a wider set of cases than the standard Circle and Popov Criteria. The results are illustrated with some numerical examples.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom