Global stabilization of feedforward systems under perturbations in sampling schedule

TL;DR

This paper demonstrates that global stabilization of feedforward nonlinear systems is achievable under variable sampling schedules with bounded periods, using specially designed discontinuous sampled-data feedback laws.

Contribution

It introduces a novel class of discontinuous feedback controllers that ensure global asymptotic stability despite sampling schedule perturbations.

Findings

Stability is maintained under any bounded sampling period.

Discontinuous feedback laws are effective for feedforward systems.

Global stabilization is achievable without approximating continuous-time controllers.

Abstract

For nonlinear systems that are known to be globally asymptotically stabilizable, control over networks introduces a major challenge because of the asynchrony in the transmission schedule. Maintaining global asymptotic stabilization in sampled-data implementations with zero-order hold and with perturbations in the sampling schedule is not achievable in general but we show in this paper that it is achievable for the class of feedforward systems. We develop sampled-data feedback stabilizers which are not approximations of continuous-time designs but are discontinuous feedback laws that are specifically developed for maintaining global asymptotic stabilizability under any sequence of sampling periods that is uniformly bounded by a certain "maximum allowable sampling period".