Finite gain lp stabilization of discrete-time LinearSystems 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. In establishing our results for p=1, we also allow the presence of certain additional external disturbance.