Mathematics / Matematik

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

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Access Right: Closed AccessAuthor: search.filters.author.Şahan, Gökhan

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 8
    Citation - Scopus: 7
    Exponential Stability and Boundedness of Nonlinear Perturbed Systems by Unbounded Perturbation Terms
    (Elsevier, 2023) Şahan, Gökhan
    We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. Contrary to most of the available conditions, we allow the coefficients to be unbounded. But instead, we put forward a condition that requires a series produced by coefficients to be limited and exponentially decaying. We perform our results on Linear time-varying systems and generalize many of the available results. & COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Structure and Stability of Bimodal Systems in R-3: Part 1
    (Azerbaijan National Academy of Sciences, 2014) Eldem, Vasfi; Şahan, Gökhan
    In this paper, the structure and global asymptotic stability of bimodal systems in R3 are investigated under a set of assumptions which simplify the geometric structure. It is basically shown that one of the assumptions being used reduces the stability problem in R3 to the stability problem in R2. However, structural analysis shows that the behavior of the trajectories changes radically upon the change of the parameters of individual subsystems. The approach taken is based on the classification of the trajectories of bimodal systems as i) the trajectories which change modes finite number of times as t ? ?, and ii) the trajectories which change modes infinite number of times as t ? ?. Finally, it is noted that this approach can be used without some of the assumptions for all bimodal systems in R3, and for bimodal systems in Rn. © 2014, Azerbaijan National Academy of Sciences. All rights reserved.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Well Posedness Conditions for Planar Conewise Linear Systems
    (SAGE Publications Inc., 2019) Şahan, Gökhan; Eldem, Vasfi
    In this study, we give well-posedness conditions for planar conewise linear systems where the vector field is not necessarily continuous. It is further shown that, for a certain class of planar conewise linear systems, well posedness is independent of the conic partition of R-2. More specifically, the system is well posed for any conic partition of R-2.
  • 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