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 - <p style="text-align: justify;">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.</p>