Stability conditions in piecewise smooth dynamical systems at a two-fold singularity

DOI10.1007/s10883-013-9164-9zbMath1283.37057OpenAlexW2017866859MaRDI QIDQ1936290

Marco Antonio Teixeira, Durval José Tonon, Alain Jacquemard

Publication date: 21 February 2013

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10883-013-9164-9

zbMATH Keywords

asymptotic stabilitystructural stabilitynon-smooth vector fieldssingularly

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Bifurcations of singular points in dynamical systems (37G10) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

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Cites Work

• Unnamed Item
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• Teixeira singularities in 3D switched feedback control systems
• Generic bifurcations of low codimension of planar Filippov systems
• The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
• Generic bifurcation of sliding vector fields
• Stability conditions for discontinuous vector fields
• Piecewise-smooth dynamical systems. Theory and applications
• The Two-Fold Singularity of Discontinuous Vector Fields
• One-Parameter Bifurcations in Planar Filippov Systems