## Abstract

For every bivariate polynomial (Formula Presented.) of bidegree (Formula Presented.), which has no zeros in the open unit bidisk, we construct a determinantal representation of the form (Formula Presented.) diagonal matrix with coordinate variables (Formula Presented.) on the diagonal and K is a contraction. We show that K may be chosen to be unitary if and only if p is a (unimodular) constant multiple of its reverse. Furthermore, for every bivariate real-zero polynomial (Formula Presented.), we provide a construction to build a representation of the form (Formula Presented.),where (Formula Presented.) are Hermitian matrices of size equal to the degree of p. A key component of both constructions is a stable factorization of a positive semidefinite matrix-valued polynomial in one variable, either on the circle (trigonometric polynomial) or on the real line (algebraic polynomial).

Original language | English |
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Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Multidimensional Systems and Signal Processing |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2016 |

## Keywords

- Determinantal representation
- Lax conjecture
- Multivariable polynomial
- Real-zero polynomial
- Self-reversive polynomial
- Stability radius
- Stable polynomial

## ASJC Scopus subject areas

- Software
- Signal Processing
- Information Systems
- Hardware and Architecture
- Computer Science Applications
- Artificial Intelligence
- Applied Mathematics