Outer Bounds for the Parametric Controllable Solution Set with Linear Shape

  • Evgenija D. PopovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9553)


We consider linear algebraic equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters, and their parametric AE-solution sets, which are defined by universal and existential quantifiers for the parameters. We present how some sufficient conditions for a parametric AE-solution set to have linear boundary can be exploited for obtaining sharp outer bounds of that parametric AE-solution set. For a parametric controllable solution set having linear boundary we present a numerical method for outer interval enclosure of the solution set. The new method has better properties than some other methods available so far.


Interval linear systems Parameter dependencies AE-solution set Controllable solution set Solution enclosure Iteration method 


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Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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