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

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.