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.