On the Disturbance Response and External Stability of a Saturating Static-Feedback-Controlled Double Integrator

We contribute to the ongoing research on the external (disturbance) response of feedback-controlled nonlinear systems by further exploring the disturbance response of a canonical system, namely a feedback-controlled double-integrator subject to actuator saturation. Precisely, we aim to delineate classes of bounded, persistent disturbances that do or do not drive the system´s state unbounded. Our key result is that a disturbance signal whose integral is bounded over all intervals - or which can be offset such that its integral is bounded - cannot drive the state unbounded. The class of such disturbance signals includes all periodic and almost-periodic ones.