## Abstract

Polynomials with zeroes in the open left half-plane of the complex plane are called Hurwitz stable. They correspond to Hurwitz matrices which arise in many important applications. A polynomial is Hurwitz stable when the Hurwitz matrix is positive semidefinite. This paper construct structured Hurwitz positive semidefinite matrix that is nearest to a given data matrix. The problem is converted into a semidefinite programming problem as well as a problem comprising of semidefined program and second-order cone problem. The duality and optimality conditions are obtained and the primal-dual algorithm is outlined. Some of the numerical issues involved will be addressed including unsymmetrical of the problem. Computational results are presented.

Original language | English |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Journal of Nonlinear and Convex Analysis |

Volume | 25 |

Issue number | 1 |

State | Published - 2024 |

### Bibliographical note

Publisher Copyright:© 2024 Yokohama Publications. All rights reserved.

## Keywords

- Conjugate gradients methods
- Hurwitz matrix
- Hurwitz polynomials
- Inexact Gauss-Newton method
- non-smooth optimization
- positive semidefinite matrix
- primal-dual interior point method
- semidefinite programming

## ASJC Scopus subject areas

- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics