# A General Class of Control Lyapunov Functions and Sampled-Data Stabilization

## TL;DR

This paper generalizes the Artstein-Sontag theorem by developing a broad class of control Lyapunov functions for sampled-data stabilization of affine nonlinear systems with nonzero drift, using Lie algebraic conditions.

## Contribution

It introduces a new class of control Lyapunov functions applicable to sampled-data feedback stabilization, extending existing theorems to more general nonlinear systems.

## Key findings

- Generalized stabilization results for affine nonlinear systems with nonzero drift
- Extended the Artstein-Sontag theorem to sampled-data control
- Provided an illustrative example demonstrating the theoretical results

## Abstract

The present work extends recent results by second author concerning sampled-data feedback stabilization for affine in the control of nonlinear systems with nonzero drift term, under the presence of a generalized control Lyapunov function associated with appropriate Lie algebraic hypotheses concerning the dynamics of the system. The main results of present work, constitute a generalization of the well-known "Artstein-Sontag" theorem on asymptotic stabilization by means of an almost smooth feedback controller. The analysis is limited to the affine single-input nonlinear systems with nonzero drift term, however, the results can easily be extended to the multi-input case. An illustrative example of the derived results is included.