A few results concerning the Hurwitz stability of polytopes of complex polynomials

作者：Bialas Stanislaw; Gora Michal^*

来源：Linear Algebra and Its Applications, 2012, 436(5): 1177-1188.

DOI：10.1016/j.laa.2011.07.042

• Zeros of polynomials
• Polytopes of polynomials
• Robust stability
• Hurwitz stability

Let C-f1,C- ... , f(m) be a polytope generated by complex polynomials f(1), ... , f(m) whose degrees differ at most by one. The main goal of this note is to provide a tool for verifying whether a polynomial family Cf-1, ... , f(m) is stable. The note extend a few important results of the robust stability theory (the Edge Theorem given by Bartlett et al. [5], its generalizations proposed by Sideris and Barmish [7] and Fu and Barmish [6] and the eigenvalue criterions of Bialas [4,11]) to more general cases concerning complex polynomial families without degree-invariant assumptions. Numerical examples are presented to complete and illustrate the results.

• 出版日期2012-3-1