On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we investigate the boundary of the attraction basinof a class of piecewise linear systems arising from anti-stable linear systemswith saturated linear state feedback. In three-dimensional cases, for this classof systems, we prove that the equilibrium points other than the origin lie onthe boundary of the attraction basin of the origin. This gives strong evidencethat the boundary of the attraction basin is homeomorphic to a sphere. Someexamples are provided to illustrate the results.
Keywords: Piecewise linear system; boundary of attraction basin; index; saturated state feedback.