Matrix-valued Hermitian Positivstellensatz, Lurking Contractions, and Contractive Determinantal Representations of Stable Polynomials Academic Article uri icon

abstract

  • We prove that every matrix-valued rational function F, which is regular on the closure of a bounded domain \(\mathcal{D}_{p}\; \mathrm{in}\;\mathbb{C}^{d}\) and which has the associated Agler norm strictly less than 1, admits a finite-dimensional contractive realization $$F(z)\;=\;D\;+\;CP(z)_{n}(I-AP(z)_n)^{-1}B$$ .

publication date

  • January 1, 2016