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Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence
Author(s) -
Kamachkin Alexander M.,
Potapov Dmitriy K.,
Yevstafyeva Victoria V.
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3567
Subject(s) - relay , control theory (sociology) , nonlinear system , mathematics , phase plane , period (music) , stability theory , plane (geometry) , mathematical analysis , control (management) , physics , computer science , geometry , power (physics) , quantum mechanics , artificial intelligence , acoustics
Summary We consider an automatic control system with relay nonlinearity and sinusoidal external influence. Sufficient conditions for the existence of periodic solutions in the case when the characteristic equation of the system has complex roots are obtained. We use an approach that permits to investigate the system analytically and prove the existence of at least one periodic solution (including asymptotically stable solution) with the period multiple to the period of external influence and two switching points on the phase plane. Copyright © 2016 John Wiley & Sons, Ltd.