Mathematics / Matematik

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

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Author: search.filters.author.Eldem, Vasfi

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Now showing 1 - 4 of 4
  • 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: 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.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Well Posedness Conditions for Bimodal Piecewise Affine Systems
    (Elsevier Ltd., 2015) Şahan, Gökhan; Eldem, Vasfi
    This paper considers well-posedness (the existence and uniqueness of the solutions) of Bimodal Piecewise Affine Systems in ℝn. It is assumed that both modes are observable, but only one of the modes is in observable canonical form. This allows the vector field to be discontinuous when the trajectories change mode. Necessary and sufficient conditions for well-posedness are given as a set of algebraic conditions and sign inequalities. It is shown that these conditions induce a joint structure for the system matrices of the two modes. This structure can be used for the classification of well-posed bimodal piecewise affine systems. Furthermore, it is also shown that, under certain conditions, well-posed Bimodal Piecewise Affine Systems in ℝn may have one or two equilibrium points or no equilibrium points.