Kharitonov’s Theorem and Bezoutians Original Research Article

An elementary proof of the Kharitonov theorem is presented. The proof is based on the concept of a Bezoutian matrix. Generally, exploiting the special structure of such matrices (e.g., Bezoutians, Toeplitz, Hankel or Vandermonde matrices, etc.) can be interesting, e.g., leading to unified approaches in different cases, as well as to further generalizations. Here the concept of the Bezoutian matrix is used to provide a unified derivation of the Kharitonov-like theorems for the continuous-time and discrete-time settings. Finally, the (block) Anderson–Jury Bezoutians are used to propose a possible technique to attack an difficult open problem related to the robust stability in the MIMO case.