Finite gain lp stabilization of discrete-time linear systems subject to actuator saturation: the case of p = 1

It has been established by Bao, Lin and Sontag (2000) that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain l_p stabilization can be achieved by linear output feedback, for every p ∈ (1, ∞] except p = 1. An explicit construction of the corresponding feedback laws was given. The feedback laws constructed also resulted in a closed-loop system that is globally asymptotically stable. This note complements the results of Bao, Lin and Sontag (2000) by showing that they also hold for the case of p = 1.