Sufficient Lie Algebraic Conditions for Sampled-Data Feedback Stabilizability of Affine in the Control Nonlinear Systems

TL;DR

This paper establishes Lie algebraic conditions under which affine nonlinear systems with drift can be stabilized using sampled-data feedback, extending classical feedback stabilization results to sampled-data contexts.

Contribution

It introduces a Lie algebraic sufficient condition for sampled-data feedback stabilizability, extending the Artstein-Sontag theorem to systems with non-zero drift.

Findings

Derived a Lyapunov-based characterization for sampled-data stabilizability.

Provided a Lie algebraic criterion extending classical feedback stabilization results.

Applied the criterion to affine nonlinear systems with non-zero drift.

Abstract

For general nonlinear autonomous systems, a Lyapunov characterization for the possibility of semi-global asymptotic stabilizability by means of a time-varying sampled-data feedback is established. We exploit this result in order to derive a Lie algebraic sufficient condition for sampled-data feedback semi-global stabilizability of affine in the control nonlinear systems with non-zero drift terms. The corresponding proposition constitutes an extension of the "Artstein-Sontag" theorem on feedback stabilization.