Robust Saturated Stabilization With Measurement Errors: From a Chain of Integrators to Feedforward Systems

This article studies the saturated stabilization problem of a chain of perturbed integrators subject to measurement errors. Inspired by the technique of nested saturation loops, a key strategy is to employ saturated set-valued maps and a generalized coordinate transformation to overcome the difficulty caused by the measurement errors. It is shown that, with the refined controller design, the closed-loop system is transformed into an interconnection of subsystems, each of which can be rendered small-disturbance input-to-state stable (ISS). The small-gain theorem is used to guarantee small-disturbance ISS of the closed-loop system with the measurement errors as the inputs. Interestingly, the proposed methodology yields new solutions to the open problems of measurement feedback control and event-triggered control for a broader class of uncertain, nonlinear feedforward systems.