Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Subject: search.filters.subject.Asymptotic stabilityWoS Q: search.filters.wosQuartile.Q2

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  • Article
    Citation - WoS: 12
    Citation - Scopus: 12
    Stability Analysis by a Nonlinear Upper Bound on the Derivative of Lyapunov Function
    (Elsevier Ltd., 2020) Şahan, Gökhan
    In this work, we give results for asymptotic stability of nonlinear time varying systems using Lyapunov-like Functions with indefinite derivative. We put a nonlinear upper bound for the derivation of the Lyapunov Function and relate the asymptotic stability conditions with the coefficients of the terms of this bound. We also present a useful expression for a commonly used integral and this connects the stability problem and Lyapunov Method with the convergency of a series generated by coefficients of upper bound. This generalizes many works in the literature. Numerical examples demonstrate the efficiency of the given approach. © 2020 European Control Association
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    The Effect of Coupling Conditions on the Stability of Bimodal Systems in R3
    (Elsevier Ltd., 2016) Eldem, Vasfi; Şahan, Gökhan
    This paper investigates the global asymptotic stability of a class of bimodal piecewise linear systems in R3. The approach taken allows the vector field to be discontinuous on the switching plane. In this framework, verifiable necessary and sufficient conditions are proposed for global asymptotic stability of bimodal systems being considered. It is further shown that the way the subsystems are coupled on the switching plane plays a crucial role on global asymptotic stability. Along this line, it is demonstrated that a constant (which is called the coupling constant in the paper) can be changed without changing the eigenvalues of subsystems and this change can make bimodal system stable or unstable.