ΔΔ-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 ΔΔ-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 ΔΔ-modulation in the sliding mode direction. The global attracting property of ΔΔ-modulated feedback offers a vivid illustration of the way sliding is achieved. Interestingly, we find that a ZOH discretization scheme of the equivalent control-based sliding mode control system with relative degree one results in only 2-periodic orbits.