TY - GEN

T1 - Dichotomy and Stability of Disturbed Systems with Periodic Nonlinearities

AU - Smirnova, Vera B.

AU - Proskurnikov, Anton V.

AU - Utina, Natalia V.

AU - Titov, Roman V.

PY - 2018/8/20

Y1 - 2018/8/20

N2 - Systems that can be decomposed as feedback interconnections of stable linear blocks and periodic nonlinearities arise in many physical and engineering applications. The relevant models e.g. describe oscillations of a viscously damped pendulum, synchronization circuits (phase, frequency and delay locked loops) and networks of coupled power generators. A system with periodic nonlinearities usually has multiple equilibria (some of them being locally unstable). Many tools of classical stability and control theories fail to cope with such systems. One of the efficient methods, elaborated to deal with periodic nonlinearities, stems from the celebrated Popov method of 'integral indices', or integral quadratic constraints; this method leads, in particular, to frequency-domain criteria of the solutions' convergence, or, equivalently, global stability of the equilibria set. In this paper, we further develop Popov's method, addressing the problem of robustness of the convergence property against external disturbances that do not oscillate at infinity (allowing the system to have equilibria points). Will the forced solutions also converge to one of the equilibria points of the disturbed system? In this paper, a criterion for this type of robustness is offered.

AB - Systems that can be decomposed as feedback interconnections of stable linear blocks and periodic nonlinearities arise in many physical and engineering applications. The relevant models e.g. describe oscillations of a viscously damped pendulum, synchronization circuits (phase, frequency and delay locked loops) and networks of coupled power generators. A system with periodic nonlinearities usually has multiple equilibria (some of them being locally unstable). Many tools of classical stability and control theories fail to cope with such systems. One of the efficient methods, elaborated to deal with periodic nonlinearities, stems from the celebrated Popov method of 'integral indices', or integral quadratic constraints; this method leads, in particular, to frequency-domain criteria of the solutions' convergence, or, equivalently, global stability of the equilibria set. In this paper, we further develop Popov's method, addressing the problem of robustness of the convergence property against external disturbances that do not oscillate at infinity (allowing the system to have equilibria points). Will the forced solutions also converge to one of the equilibria points of the disturbed system? In this paper, a criterion for this type of robustness is offered.

UR - http://www.scopus.com/inward/record.url?scp=85053438562&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/dichotomy-stability-disturbed-systems-periodic-nonlinearities

U2 - 10.1109/MED.2018.8443008

DO - 10.1109/MED.2018.8443008

M3 - Conference contribution

AN - SCOPUS:85053438562

SN - 9781538678909

SP - 903

EP - 908

BT - MED 2018 - 26th Mediterranean Conference on Control and Automation

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 26th Mediterranean Conference on Control and Automation

Y2 - 19 June 2018 through 22 June 2018

ER -