Disturbance tolerance and rejection of discrete-time stochastic systems with saturating actuators

This paper considers the problems of disturbance tolerance and disturbance rejection capabilities of discrete-time stochastic systems with saturating actuators. We consider two classes of disturbances whose energy and magnitudes are bounded. A simple condition is given under which any trajectories starting from a certain ellipsoid will remain inside an outer ellipsoid. Invariant sets of criteria are presented. Based on the derived condition, the problems of disturbance tolerance and rejection capabilities of the closed-loop system under a given state feedback law are solved. The effectiveness of these results is demonstrated by a simulation example.