arXiv subjects

I. Zaballa

Publications and source records attributed to I. Zaballa.

3 recordsLinked to original sources

arXiv2025

A Local Parametrization of the State-Feedback Matrices in the Pole Assignment Problem

Given a controllable system $(F,G)$, a local parametrization is obtained for the set of feedback gain matrices $K$ such that the state matrix, $F+GK$, of the closed loop system is in a prescribed similarity class. It is shown that this set can be endowed with the structure of a differentiable manifold whose dimension is also computed. Then a local parametrization and a local system of coordinates is provided using a diffeomorphism between this set of state feedback matrices and the orbit space of a set of truncated observability matrices via de action of a Lie group.

math.OC↗

arXiv2019

On variation of eigenvalues of birth and death matrices and random walk matrices

The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open problem concerning the variation of eigenvalues of these matrices. Keywords: Birth and death matrices, random walk matrices, eigenvalues, monotonicity

math.PR↗

arXiv2009

Gravitational reheating in quintessential inflation

We provide a detailed study of gravitational reheating in quintessential inflation generalizing previous analyses only available for the standard case when inflation is followed by an era dominated by the energy density of radiation. Quintessential inflation assumes a common origin for inflation and the dark energy of the Universe. In this scenario reheating can occur through gravitational particle production during the inflation-kination transition. We calculate numerically the amount of the radiation energy density, and determine the temperature $T_*$ at which radiation starts dominating over kination. The value of $T_*$ is controlled by the Hubble parameter $H_0$ during inflation and the transition time $Δt$, scaling as $H_0^2 [\ln(1/H_0Δt)]^{3/4}$ for $H_0 Δt \ll1$ and $H_0^2 (H_0 Δt)^{-c}$ for $H_0Δt \gg 1$. The model-dependent parameter $c$ is found to be around 0.5 in two different parametrizations for the transition between inflation and kination.

hep-ph↗