Stability and multiscroll attractors of control systems via the abscissa
type: Item
instance of: scholarly article
title: Stability and multiscroll attractors of control systems via the abscissa
zbMATH Open document ID: 1426.93248
DOI: 10.1155/2017/6743734
author: Edgar-Cristian Díaz-González
author: Baltazar Aguirre-Hernández
author: Jorge-Antonio López-Rentería
author: E. Campos-Cantón
author: Carlos-Arturo Loredo-Villalobos
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: We present an approach to generate multiscroll attractors via destabilization of piecewise linear systems based on Hurwitz matrix in this paper. First we present some results about the abscissa of stability of characteristic polynomials from linear differential equations systems; that is, we consider Hurwitz polynomials. The starting point is the Gauss-Lucas theorem, we provide lower bounds for Hurwitz polynomials, and by successively decreasing the order of the derivative of the Hurwitz polynomial one obtains a sequence of lower bounds. The results are extended in a straightforward way to interval polynomials; then we apply the abscissa as a measure to destabilize Hurwitz polynomial for the generation of a family of multiscroll attractors based on a class of unstable dissipative systems (UDS) of affine linear type.
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 6972370
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6743734
OpenAlex ID: W2745506553
cites work: Q4847220
cites work: Q3254327
cites work: Inertia characteristics of self-adjoint matrix polynomials
cites work: Q5546070
cites work: Q4180603
cites work: Computation of the minimum destabilizing volume for interval and affine families of polynomials
cites work: On the complete instability of interval polynomials
cites work: On Kharitonov's theorem without invariant degree assumption.
cites work: A dual result to Kharitonov's theorem
cites work: The Kharitonov theorem with degree drop
cites work: Sufficient algebraic conditions for stability of cones of polynomials
cites work: Algebraic test for the Hurwitz stability of a given segment of polynomials
cites work: A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices
cites work: The boundary crossing theorem and the maximal stability interval
cites work: Q5485394
cites work: Bibliography on robust control
cites work: Q5610653
cites work: Lower Bounds to the Abscissa of Stability of a Stable Polynomial from Symmetric Functions
cites work: Q3692714
cites work: Upper Bounds for the Abscissa of Stability of a Stable Polynomial
cites work: Determination of a neighborhood of the imaginary axis which is disjoint from the spectrum of a real polynomial
cites work: Multiscroll attractors by switching systems
cites work: Attractors generated from switching unstable dissipative systems
cites work: Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method
cites work: A family of hyperchaotic multi-scroll attractors in \(\mathbb{R}^n\)
cites work: \(n\)-scroll chaotic attractors from saturated function series employing CCII\(+\)s
cites work: Generation of n-double scrolls (n=1, 2, 3, 4,...)
cites work: FAMILIES OF SCROLL GRID ATTRACTORS
cites work: Q4175201
cites work: Computation of the abscissa of stability by repeated use of the Routh test
cites work: A criterion of approximation for the method of inequalities
cites work: A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems
cites work: Maximal unstable dissipative interval to preserve multi-scroll attractors via multi-saturated functions
description: scientific article; zbMATH DE number 6972370