The hybrid matching of Hurwitz systems
Abstract
In this paper we study planar hybrid systems composed by two stable linear systems, defined by Hurwitz matrices, in addition with a jump that can be a piecewise linear, a polynomial or an analytic function. We provide an explicit analytic necessary and sufficient condition for this class of hybrid systems to be asymptotically stable. We also prove the existence of limit cycles in this class of hybrid systems. Our results can be seen as generalizations of results already obtained in the literature. This was possible due to an embedding of piecewise smooth vector fields in a hybrid structure.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Stability and Control of Uncertain Systems
Polynomial and algebraic computation
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 560
- Issue
- 1
- Pages
- 130492–130492
- Publication date
- 5 February 2026
- Language
- EN