Abstract
In this paper, algebraic tests are proposed to establish asymptotic stability of parametric linear systems assuming that the parameters lie in a given variety. In particular, by using tools borrowed from algebraic geometry, necessary and sufficient condition are proposed to test whether a continuous-time or a discrete-time linear parametric system is asymptotically stable for all the specializations belonging to a given variety. Both the cases of zero dimensional and non-zero dimensional varieties are considered.
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