linear systems dependent data AE solution set tolerable solution set controllable solution set Department of Biomathematics
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
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.