full
search.png

Search

close.png

Cancel

Volume 5, Issue 2
On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems

Yuhong Zhang, Weisheng Huang & Xiaosong Yang

DOI: 10.12150/jnma.2023.228

J. Nonl. Mod. Anal., 5 (2023), pp. 228-246.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

Preview Full PDF 632 6246

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper, we investigate the boundary of the attraction basin of a class of piecewise linear systems arising from anti-stable linear systems with saturated linear state feedback. In three-dimensional cases, for this class of systems, we prove that the equilibrium points other than the origin lie on the boundary of the attraction basin of the origin. This gives strong evidence that the boundary of the attraction basin is homeomorphic to a sphere. Some examples are provided to illustrate the results.

  • Keywords

Piecewise linear system, boundary of attraction basin, index, saturated state feedback.

  • AMS Subject Headings

34D20, 34C37, 93D15, 58J20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JNMA-5-228, author = {Zhang , YuhongHuang , Weisheng and Yang , Xiaosong}, title = {On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {2}, pages = {228--246}, abstract = {

In this paper, we investigate the boundary of the attraction basin of a class of piecewise linear systems arising from anti-stable linear systems with saturated linear state feedback. In three-dimensional cases, for this class of systems, we prove that the equilibrium points other than the origin lie on the boundary of the attraction basin of the origin. This gives strong evidence that the boundary of the attraction basin is homeomorphic to a sphere. Some examples are provided to illustrate the results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.228}, url = {http://global-sci.org/intro/article_detail/jnma/21923.html} }
TY - JOUR T1 - On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems AU - Zhang , Yuhong AU - Huang , Weisheng AU - Yang , Xiaosong JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 228 EP - 246 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.228 UR - https://global-sci.org/intro/article_detail/jnma/21923.html KW - Piecewise linear system, boundary of attraction basin, index, saturated state feedback. AB -

In this paper, we investigate the boundary of the attraction basin of a class of piecewise linear systems arising from anti-stable linear systems with saturated linear state feedback. In three-dimensional cases, for this class of systems, we prove that the equilibrium points other than the origin lie on the boundary of the attraction basin of the origin. This gives strong evidence that the boundary of the attraction basin is homeomorphic to a sphere. Some examples are provided to illustrate the results.

Yuhong Zhang, Weisheng Huang & Xiaosong Yang. (2023). On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems. Journal of Nonlinear Modeling and Analysis. 5 (2). 228-246. doi:10.12150/jnma.2023.228
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard