Invariant manifolds for nonsmooth systems with sliding mode

D. Weiss, T. Küpper and H.A. Hosham

Mathematics and Computers in Simulation (MATCOM), 2015, vol. 110, issue C, 15-32

Abstract: Invariant manifolds play an important role in the study of Dynamical Systems, since they help to reduce the essential dynamics to lower dimensional objects. In that way, a bifurcation analysis can easily be performed. In the classical approach, the reduction to invariant manifolds requires smoothness of the system which is typically not given for nonsmooth systems. For that reason, techniques have been developed to extend such a reduction procedure to nonsmooth systems. In the present paper, we present such an approach for systems involving sliding motion. In addition, an analysis of the reduced equation shows that the generation of periodic orbits through nonlinear perturbations which is usually related to Hopf bifurcation follows a different type of bifurcation if nonsmooth elements are present, since generically symmetry is broken by the nonsmooth terms.

Keywords: Invariant manifold; Sliding motion; Nonlinear piecewise dynamical systems; Non-smooth systems; Invariant cones; Periodic orbits; Generalized Hopf bifurcation (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037847541400041X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:110:y:2015:i:c:p:15-32

DOI: 10.1016/j.matcom.2014.02.004

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().