Browsing by Author "Eldem,V."

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    Citation Count: 1
    On the feasibility problem of linear matrix inequalities
    (Institute of Applied Mathematics of Baku State University, 2011) Eldem,V.; Şahin,Ş.
    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.
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    Citation Count: 7
    Structure and stability of bimodal systems in ℝ3: Part 1
    (Azerbaijan National Academy of Sciences, 2014) Eldem,V.; Şahan,G.
    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.