Abstract
In this paper, we present a framework for studying distributed averaging dynamics over general state spaces. We define several modes of ergodicity and consensus for such dynamics and show that, unlike for a finite dimensional space, these modes are not equivalent. Motivated by the role of the infinite flow property in ergodicity in finite dimensional spaces, we define the infinite flow property for averaging dynamics in general state spaces. We show that this property is a necessary condition for the weakest form of ergodicity. Also, we characterize a class of quadratic Lyapunov comparison functions for certain averaging dynamics and provide a relation capturing the decrease of these functions along the trajectories of the dynamics.
| Original language | English (US) |
|---|---|
| Article number | 6426900 |
| Pages (from-to) | 62-67 |
| Number of pages | 6 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| DOIs | |
| State | Published - 2012 |
| Externally published | Yes |
| Event | 51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: Dec 10 2012 → Dec 13 2012 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization