Geometric properties of some sets of stable polynomials and entire functions (Q2741139)

A given polynomial \( a(s)=a_{0}+a_{1}s+...+a_{n-1}s^{n-1}+s^{n} \) with real coefficients \( a_{i} \), \( i=0,1,...,n-1 \), is called a stable or Hurwitz polynomial if all its roots have a negative real part. The polynomial \( a(\cdot) \) can be identified with the point \( a=(a_{0},a_{1},...,a_{n-1})\in\mathbb{R}^{n} \). By \(H^{n}\subset\mathbb{R}^{n} \) we denote the set of all Hurwitz polynomials of degree \( n \). In the paper the authors present, without proofs, some results obtained by mathematicians of the Universidad Nacional del Sur, at Bahia Blanca, Argentina, during the last few years and related to the convexity properties of \( H^{n} \), simplicial approximation of the boundary \( \partial H^{n} \) and stability. The results presented in the paper may have applications in robust control theory and in the stability theory of differential systems.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00030].