Stability and robustness for discrete-time systems with control signal saturation

Abstract

All practical control systems exhibit control signal saturation. The effect that this saturation has on the control system performance, especially stability and robustness, can be significant and must be understood at the controller design stage. This paper presents conditions for global asymptotic stability and measures of stability robustness for such systems. These are demonstrated through simulation examples, and it is shown how an understanding of the stability conditions can inform the controller design process. The off-axis circle criterion is used as the basis for a sufficient condition for stability, and it is argued that this is not overly restrictive in practice. The derivations are carried out in discrete time, and servo-system control is envisaged as an important application area for the techniques; however, the results are applicable more widely.