Predictive switching logic schemes are considered whereby a feedback-gain is switched-on at any time from a family of candidate feedback-gains so as to control a discrete-time input-saturated LTI system possibly subject to persistent bounded disturbances of unknown arbitrary magnitude. It is constructively shown that such schemes do exist which ensure, along with good tracking performance, global asymptotic and semi-global exponential stability in the noiseless case, as well as finite l(infinity)-induced gain to the disturbance-to-state map, whenever the structure of the disturbed plant can make such properties conceptually achievable. viz., the disturbance, which enters an Asymptotically Null-Controllable with Bounded Input (ANCBI) system acts directly only on the stable modes. while the critically unstable ones are indirectly affected by the disturbance only via the feedback controls. More generally. in ANCBI systems general disturbances of suitably bounded magnitude can also be handled by the scheme, provided that the, switching logic be equipped with an appropriate hysteresis facility. (C) 2004 Elsevier Ltd. All rights reserved.