We study dynamical systems that switch between two different vector fields depending on a discrete variable. If the two vector fields have linearly unstable fixed points and the switch is subject to a hysteresis and to a delay one expects the system to switch periodically back and forth between the two vector fields, always switching at certain submanifolds of the state space. This is true as long as the delay is sufficiently small. When the delay reaches a problem-dependent critical value so-called event collisions occur. We show that at these event collisions the switching manifolds can increase their dimension, giving rise to higher-dimensional dynamics near the periodic orbit than expected. In many practical applications such as control engineering the dynamical system has additional symmetry, which adds difficulty in the analysis because event collisions generically occur at several points along the periodic orbit simultaneously.
|Publication status||Accepted/In press - Apr 2006|
Bibliographical noteAdditional information: Preprint version of a paper accepted for presentation at the 6th IFAC Workshop on Time-Delay Systems, L’Aquila (Italy), 2006.
Sponsorship: The research of J.Sieber is supported by EPSRC grant GR/R72020/01.
- non-smooth map
- delayed switch
- hybrid dynamical system