A Poincaré-Bendixson theorem for hybrid systems

DOI10.3934/mcrf.2019028zbMath1442.34072arXiv1801.09014OpenAlexW2964071034MaRDI QIDQ2175611

Yanyan Li

Publication date: 29 April 2020

Published in: Mathematical Control and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.09014

zbMATH Keywords

hybrid systemsPoincaré mapPoincaré-Bendixson theoremstability of periodic orbitshybrid flows

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Hybrid systems of ordinary differential equations (34A38)

Related Items

Symmetries and periodic orbits in simple hybrid Routhian systems ⋮ A Poincaré-Bendixson theorem for hybrid dynamical systems on directed graphs ⋮ Conley's Fundamental Theorem for a Class of Hybrid Systems ⋮ Limit cycle analysis of a class of hybrid gene regulatory networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Qualitative theory of hybrid dynamical systems.
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
• Geometric formulation of mechanical systems with one-sided constraints
• Hamiltonian theory of constrained impulsive motion
• Mechanical systems subjected to impulsive constraints
• Asymptotically stable walking for biped robots: analysis via systems with impulse effects
• The Dynamics of Legged Locomotion: Models, Analyses, and Challenges