Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Conference Object Existence and Uniqueness of Solution for Discontinuous Conewise Linear Systems(Elsevier, 2020) Şahan, GökhanIn this study, we give necessary and sufficient conditions for well posedness of Conewise Linear Systems in 3-dimensional space where the vector field is allowed to be discontinuous. The conditions are stated using the subspaces derived from subsystem matrices and the results are compared with the existing conditions given in the literature. We show that even we don't have a fixed structure on system matrices as in bimodal systems, similar subspaces and numbers again determines well posedness. Copyright (C) 2020 The Authors.Article Citation - WoS: 2Citation - Scopus: 2Well Posedness Conditions for Planar Conewise Linear Systems(SAGE Publications Inc., 2019) Şahan, Gökhan; Eldem, VasfiIn 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: 6Citation - Scopus: 6Well Posedness Conditions for Bimodal Piecewise Affine Systems(Elsevier Ltd., 2015) Şahan, Gökhan; Eldem, VasfiThis 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.