Browsing by Author "Eldem, Vasfi"

Now showing 1 - 7 of 7

Citation Count: 3
The effect of coupling conditions on the stability of bimodal systems in R³
(Elsevier, 2016) Eldem, Vasfi; Eldem, Vasfi
This paper investigates the global asymptotic stability of a class of bimodal piecewise linear systems in R-3. 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. (C) 2016 Elsevier B.V. All rights reserved.
Citation Count: 0
Necessary and sufficient conditions for global asymptotic stability of a class of bimodal systems with discontinuous vector fields
(Oxford Univ Press, 2018) Oner, Isil; Eldem, Vasfi
In this article, we derive the necessary and sufficient conditions for global asymptotic stability of a class of bimodal piecewise linear systems in R-3, where first mode has complex eigenvalues and the second mode has only real eigenvalues. The vector field is allowed to be discontinuous on the switching plane. The effect of discontinuity is illustrated by two examples.
Citation Count: 7
A note on the stability of bimodal systems in with discontinuous vector fields
(Taylor & Francis Ltd, 2015) Eldem, Vasfi; Eldem, Vasfi
This paper presents the necessary and sufficient conditions for global asymptotic stability of a class of bimodal piecewise linear systems in [GRAPHICS] . The approach being used allows the vector field to be discontinuous on the switching plane. It is shown that the discontinuity of the vector field plays a crucial role in global asymptotic stability. This point is illustrated by examples, where the change in the discontinuity of the vector field (without changing the eigenvalues of subsystems) can cause the system to be globally asymptotically stable or unstable.
Citation Count: 1
ON THE FEASIBILITY PROBLEM OF LINEAR MATRIX INEQUALITIES
(Ministry Communications & High Technologies Republic Azerbaijan, 2011) Eldem, Vasfi; Sahin, Seyhan
Various problems in system and control theory can be numerically solved by translating them into linear matrix inequality problems. Although there are numerous software packages that solve LMIs, they provide us only one solution if the feasibility range is nonempty. The objective of this research is to develop a methodology for partial characterization of the feasibility region of a given LMI, and to define this region via conic combinations of a finite number of vectors. Towards the end, we first introduce an inner cone for a given LMI with at least one strictly definite element. Then, we define an outer cone for a given second order LMI with nondefinite elements, and propose a procedure for refining this cone so that it will intersect the feasibility region of the given LMI.
Citation Count: 7
STRUCTURE AND STABILITY OF BIMODAL SYSTEMS IN R³: PART 1
(Ministry Communications & High Technologies Republic Azerbaijan, 2014) Eldem, Vasfi; Sahan, Gokhan
In this paper, the structure and global asymptotic stability of bimodal systems in R-3 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 R-3 to the stability problem in R-2. 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 -> infinity, and ii) the trajectories which change modes infinite number of times as t -> infinity. Finally, it is noted that this approach can be used without some of the assumptions for all bimodal systems in R-3, and for bimodal systems in R-n.
Citation Count: 6
Well posedness conditions for Bimodal Piecewise Affine Systems
(Elsevier, 2015) Sahan, Gokhan; Eldem, Vasfi
This paper considers well-posedness (the existence and uniqueness of the solutions) of Bimodal Piecewise Affine Systems in R-n. 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 R-n may have one or two equilibrium points or no equilibrium points. (C) 2015 Elsevier B.V. All rights reserved.
Citation Count: 2
Well posedness conditions for planar conewise linear systems
(Sage Publications Ltd, 2019) Sahan, Gokhan; 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.