Stabilization of Discrete-Time Linear Systems Subject to Input Saturation and Multiple Unknown Constant Delays

In this technical note, we study the semi-global stabilization of general linear discrete-time critically unstable systems subject to input saturation and multiple unknown input delays. Based on a simple frequency-domain stability criterion, we find upper bounds for delays that are inversely proportional to the argument of open-loop eigenvalues on the unit circle. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problems.