Complex dynamics of systems under delta-modulated feedback
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 1888-1902 |
| Journal / Publication | IEEE Transactions on Automatic Control |
| Volume | 51 |
| Issue number | 12 |
| Publication status | Published - Dec 2006 |
Link(s)
Abstract
In this paper, we cast the design of Δ-modulated control of a high-order system into the study of control Lyapunov functions. We classify the complex dynamics of the closed-loop system in three cases. In the first case, we show how Δ-modulated feedback introduces a finite set of globally attracting periodic points. We find the numbers and periods of all possible such periodic orbits. In addition, we characterize the attracting region for each of such periodic points. In the second case, we show that there is a maximal "stabilizable" region, and inside this region, there is a local attractor. In the last case, we show that all the states stabilizable by the Δ-modulated feedback constitute a Cantor set. This Cantor set is a repeller, and the closed-loop system is chaotic on the Cantor set. © 2006 IEEE.
Research Area(s)
- Attracting region, Attractor, Cantor set, Chaos, Control Lyapunov function, Delta-modulation, Repeller
Citation Format(s)
Complex dynamics of systems under delta-modulated feedback. / Gai, Rudong; Xia, Xiaohua; Chen, Guanrong.
In: IEEE Transactions on Automatic Control, Vol. 51, No. 12, 12.2006, p. 1888-1902.
In: IEEE Transactions on Automatic Control, Vol. 51, No. 12, 12.2006, p. 1888-1902.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
