Global dynamics of unbalanced delta-modulated feedback-controlled discrete-time systems

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)635-679
Journal / PublicationDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Issue number5
Publication statusPublished - Oct 2006


In this paper, a control policy called Unbalanced Δ-Modulated Feedback (UDMF) is proposed. For one-dimensional discrete-time systems with a parameter 0 2/Δ1. Corresponding to each parameter γ of the denumerable set, systems of Type I have no periodic orbits and, in this case, every orbit is dense in the state interval [-Δ1, Δ2). To each of the other rate values of γ, systems of Type I all have an unique periodic orbit. In particular, the structural property of the periodic motion is robust; that is, there exists an interval including this value γ such that all parameters in this interval are corresponding to those periodic orbits of the same structural property. For the case of a = 1, all points in the interval [- Δ1, Δ2) are n-periodic with n ≥ 3 when γ is a rational number, and every orbit is dense in the interval [-Δ1, Δ2) when γ is an irrational number. Moreover, every such unique periodic orbit is globally attracting for both types of systems. Copyright © 2006 Watam Press.

Research Area(s)

  • Global attractor, Periodic orbit, Unbalanced Δ-modulated feedback