Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3380

 Title: Explicit Description of AE Solution Sets to Parametric Linear Systems Other Titles: Явно описание на AE множества от решения на параметрични линейни системи Authors: Popova, Evgenija D. Keywords: linear systemsdependent dataAE solution settolerable solution setcontrollable solution setDepartment of Biomathematics Issue Date: Dec-2011 Publisher: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences Citation: Preprint Series/Report no.: 2011;7 Abstract: Consider linear systems whose input data are linear functions of uncertain parameters varying within given intervals. We are interested in an explicit description of the so-called AE parametric solution sets (where all universally quantified parameters precede all existentially quantified ones) by a set of inequalities not involving the parameters. This work presents how to obtain explicit description of AE parametric solution sets by combining a modified Fourier-Motzkin-type elimination of existentially quantified parameters with the elimination of the universally quantified parameters. Some necessary (and sufficient) conditions for existence of non-empty AE parametric solution sets are discussed, as well as some properties of the parametric AE solution sets, e.g. shape of the solution set and some inclusion relations. Explicit description of particular classes of AE parametric solution sets (tolerable, controllable, any 2D) are given. Numerical examples illustrate the solution sets and their properties. Mathematics Subject Classification (2000): 65F05, 65G99. Description: [Popova Evgenija D.; Попова Евгения Д.] URI: http://hdl.handle.net/10525/3380 Appears in Collections: Preprints

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