Delta-Modulated feedback in discretization of sliding mode control

Modulated feedback control introduces periodicity. The global attracting property of the periodic points is established for a simple scalar discrete-time system under ∆-modulated feedback. Attracting regions of the periodic points are also characterized. When the discretization effects of the equivalent control based sliding mode control systems are studied, we show that the zero-order-hold discretization gives rise to ∆-modulation in the sliding mode direction. The global attracting property of ∆-modulated feedback offers a vivid illustration of the way sliding happens. Interestingly, we find that a ZOH discretization scheme of the equivalent control based sliding mode control system with relative degree one results in only two-periodic orbits. Copyright 2005 IFAC