Abstract
SummaryThis paper aims to assess the stability of a polytope of linear systems by their vertices. These results are based on the Hermite‐Biehler and Edge theorems. A sufficient condition satisfying a constraint on the even (or odd) part of the closed‐loop characteristic polynomials associated with the stabilization of its vertices is proved. Finally, a constructive method to stabilize a polytope of plants with simultaneous and robust linear time‐invariant controllers is established.
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