A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Aguirre‐Hernández, Baltazar; Villafuerte-Segura, Raúl; Luviano‐Juárez, Alberto; Loredo-Villalobos, Carlos Arturo; Díaz-González, Edgar Cristian

doi:10.1155/2020/9410315

Cited by 4 publications

(1 citation statement)

References 369 publications

(347 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to the applications of the components of pre‐twisted differentiability function for solving classical PDEs of the mathematical physics, applications to Elasticity are possible; see Lu 10 and preprint arXiv: 1601.01626. More functional analysis techniques, complex analysis, and matrix theory are applied in Aguirre‐Hernández et al 11 and references therein.…”

Section: Discussionmentioning

confidence: 99%

On solutions of PDEs by using algebras

López‐González

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

The components of complex analytic functions define solutions for the Laplace's equation, and in a simply connected domain, each solution of this equation is the first component of a complex analytic function. In this paper, we generalize this result; for each PDE of the form Auxx+Buxy+Cuyy=0, and for each affine planar vector field φ, we give an algebra 𝔸 with unit e = e1, with respect to which the components of all functions of the form scriptL1.5pt∘1.5ptφ are all the solutions for this PDE, where scriptL is differentiable in the sense of Lorch with respect to 𝔸. Solutions are also constructed for the following equations: Auxx+Buxy+Cuyy+Dux+Euy+Fu=0, 3rd‐order PDEs, and 4th‐order PDEs; among these are the bi‐harmonic, the bi‐wave, and the bi‐telegraph equations.

show abstract

Section: Discussionmentioning

confidence: 99%

On solutions of PDEs by using algebras

López‐González

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Stability analysis of polynomials with an approach of differential topology

López‐Flores,

Aguirre‐Hernández,

Frías‐Armenta

2024

Asian Journal of Control

View full text Add to dashboard Cite

SummaryIn this paper, we study the Hurwitz stability of polynomials. By considering that a degree Hurwitz polynomial has its corresponding Markov parameters, we define the set in Section 3, we also define . Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that is a fiber bundle with a base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices.

show abstract