New Results on Sampled-Data Feedback Stabilization for Autonomous Nonlinear Systems

TL;DR

This paper establishes new sufficient conditions for the global asymptotic stabilization of nonlinear autonomous systems using sampled-data feedback, extending classical theorems and addressing interconnected systems.

Contribution

It extends the Artstein-Sontag theorem to sampled-data feedback and provides conditions for stabilizing interconnected nonlinear systems.

Findings

Extended Artstein-Sontag theorem for sampled-data feedback

Derived Lie algebraic conditions for interconnected systems

Established global asymptotic stabilization criteria

Abstract

Sufficient conditions are established for sampled-data feedback global asymptotic stabilization for nonlinear autonomous systems. One of our main results is an extension of the well known Artstein-Sontag theorem on feedback stabilization concerning affine in the control systems. A second aim of the present work is to provide sufficient conditions for sampled-data feedback asymptotic stabilization for two interconnected nonlinear systems. Lie algebraic sufficient conditions are derived for the case of affine in the control interconnected systems without drift terms.