No abstract

This 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.

This paper presents the design of a simultaneous compensator for a segment of systems based on an interpolation method with stable polynomial interpolants. This problem leads to formulate conditions of polynomial divisibility in the case of the simultaneous control as a polynomial interpolation issue. Finally, an algorithm permitting to compute a simultaneous controller stabilizing a segment of systems is given.