In this paper we go on with the analysis of the asymptotic behavior of Lur'e-type systems with periodic nonlinearities and infinite sets of equilibria. It is well known by now that this class of systems can not be efficiently investigated by the second Lyapunov method with the standard Lur'e-Postnikov function ("a quadratic form plus an integral of the nonlinearity"). So several new methods have been elaborated within the framework of Lyapunov direct method. The nonlocal reduction technique proposed by G.A. Leonov in the 1980s is based on the comparison principle. The feedback system is reduced to a low-order system with the same nonlinearity and known asymptotic behavior. Its trajectories are injected into Lyapunov function of the original system. In this paper we develop the method of nonlocal reduction. We propose a new Lyapunov-type function which involves both the trajectories of the comparison system and a modified Lur'e-Postnikov function. As a result a new frequency-algebraic criterion ensuring the convergence of every solution to some equilibrium point is obtained.
Translated title of the contributionПрименение метода нелокального сведения Леонова для исследования точечной устойчивости фазовых систем
Original languageEnglish
Title of host publicationProceedings of 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), STAB 2020
EditorsValentin N. Tkhai
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages4
ISBN (Electronic)978-1-7281-6705-3
ISBN (Print)978-1-7281-6706-0
DOIs
StatePublished - Jun 2020
Event15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB): Pyatnitskiy's Conference - ИПУ РАН, Москва, Russian Federation
Duration: 2 Jun 20205 Jun 2020
Conference number: 15

Conference

Conference15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)
Abbreviated titleSTAB 2020
Country/TerritoryRussian Federation
CityМосква
Period2/06/205/06/20

    Scopus subject areas

  • Mechanical Engineering
  • Control and Optimization
  • Control and Systems Engineering

    Research areas

  • Lyapunov-type function, Nonlinear system, periodic nonlinearity, pointwise stability

ID: 71409527