Matrix-valued Hermitian Positivstellensatz, Lurking Contractions, and Contractive Determinantal Representations of Stable Polynomials
Matrix-valued Hermitian Positivstellensatz, Lurking Contractions, and Contractive Determinantal Representations of Stable Polynomials
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矩阵值 Hermitian Positivstellensatz、潜伏收缩和稳定多项式的收缩行列式表示
DOI：
10.1007/978-3-319-31383-2_7
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
H. Woerdeman
中科院分区：
文献类型：
--
作者：
A. Grinshpan;Dmitry S. Kaliuzhnyi;V. Vinnikov;H. Woerdeman
证明了在有界域闭包上正则且Agler范数严格小于1的矩阵值有理函数F允许有限维压缩实现
$$F(Z)\；=\；D\；+\；CP(Z)_{n}(I-AP(Z)_n)^{-1}B$$
。
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
$$F(z)\;=\;D\;+\;CP(z)_{n}(I-AP(z)_n)^{-1}B$$
.