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

•
• Overview
•
• Research
•
• View All
•

### 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