Complex dynamics of systems under delta-modulated feedback

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1888-1902
Journal / PublicationIEEE Transactions on Automatic Control
Issue number12
Publication statusPublished - Dec 2006


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