Structural properties of a class of functions arising in stability theory

Abstract

Functions like positive para-odd and complex discrete reactance functions play important roles in both Routh-Hurwitz and Schur-Cohn stability theories. Other functions like circular symmetric and circular antisymmetric have impacted stability problems in various ways. It is the objective of this paper to highlight some of the important structural properties of these functions and relations between them, leading to new characterizations of antisymmetric and complex discrete reactance functions both in terms of circular symmetric and circular antisymmetric functions.

Subject Classification: (2010):

• Primary 37C75
• 93C15
• Secondary 93D
• 30E

Keywords:

• Hurwitz polynomials
• Asymptotic stability
• Routh array
• Extended routh array
• Positive para-odd functions
• Complex discrete reactance functions