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Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle | | Ian R. Manchester
; Jean-Jacques E. Slotine
; | | Date: |
20 Sep 2012 | | Abstract: | Stable periodic behavior is the desired behavior of many robotic systems,
such as walking robots, swimming robots, and other biologically inspired
systems. Designing and verifying controllers for stable periodic behaviour is
significantly more challenging than for equilibria. We study pointwise
contraction conditions for an autonomous system which imply the existence and
global stability of a limit cycle in a compact manifold. Unlike methods based
on Lyapunov theory, our condition does not require knowledge of the location of
the limit cycle in state-space. This allows straightforward extension to
robustness via parameter-dependent certificates, and compositions of systems in
feedback and serial interconnections. This new criterion also has interesting
connections to contraction theory for trajectories, orbital stability analysis
via transverse linearization, and topological facts about regions of attraction
of limit cycles. | | Source: | arXiv, 1209.4433 | | Services: | Forum | Review | PDF | Favorites | |
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