Robust Hurwitz stability of polytopes of complex polynomials

The main goal of this note is to provide a complete tool for verifying whether polytopes of complex polynomials whose degrees differ at most by one are Hurwitz stable. The results extend some classical theorems, such as the Edge Theorem given by Bartlett, Hollot and Huang (1988), its generalizations proposed by Sideris and Barmish (1989), Fu and Barmish (1989), and the eigenvalue criterion given by Bia las (1985), to more general cases concerning complex polynomial families without degree– invariant assumptions. Numerical examples are presented to complete and illustrate the results. a) The School of Banking and Management, 4 Armii Krajowej St., 30-150 Kraków, Poland e-mail address: [email protected], Tel.: +48 126173556; fax +48 126173165. b) Corresponding author. Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland e-mail address: [email protected], Tel.: +48 126173556; fax +48 126173165.