Abstract
The analysis of incremental stability properties typically involves measuring the distance between any pair of solutions of a given dynamical system, corresponding to different initial conditions, at the same time instant. This approach is not directly applicable for hybrid systems in general. Indeed, hybrid systems generate solutions that are defined with respect to hybrid times, which consist of both the continuous time elapsed and the discrete time, that is the number of jumps the solution has experienced. Two solutions of a hybrid system do not a priori have the same time domain, and we may therefore not be able to compare them at the same hybrid time instant. To overcome this issue, we invoke graphical closeness concepts. We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively. Examples are provided throughout the paper to illustrate these definitions, and the relations between these three incremental stability notions are investigated. The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems.
Original language | English |
---|---|
Title of host publication | Proceedings of the 2015 IEEE 54th Annual Conference on Decision and Control |
Editors | Y. Ohta, M. Sampei, A. Astolfi |
Place of Publication | Piscataway, NJ, USA |
Publisher | IEEE |
Pages | 5544-5549 |
ISBN (Electronic) | 978-1-4799-7886-1 |
DOIs | |
Publication status | Published - 2015 |
Event | 54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: 15 Dec 2015 → 18 Dec 2015 Conference number: 54 |
Conference
Conference | 54th IEEE Conference on Decision and Control, CDC 2015 |
---|---|
Abbreviated title | CDC 2015 |
Country/Territory | Japan |
City | Osaka |
Period | 15/12/15 → 18/12/15 |
Keywords
- Asymptotic stability
- Convergence
- Discrete-time systems
- Euclidean distance
- Hybrid power systems
- Stability analysis
- Time-domain analysis