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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.
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.

Mathematics / Matematik