# On exponential stabilization of nonholonomic systems with time-varying drift

## TL;DR

This paper develops a method for exponentially stabilizing a class of nonlinear control systems with time-varying drift using periodic feedback controls, ensuring stability under certain conditions.

## Contribution

It introduces an explicit parametrization of periodic time-varying feedback controllers for stabilization of nonlinear systems with bounded drift, under a non-resonance assumption.

## Key findings

- Controllers guarantee exponential stability when the period is sufficiently small
- Method successfully stabilizes an underwater vehicle model
- Method applied to stabilize a front-wheel drive car

## Abstract

A class of nonlinear control-affine systems with bounded time-varying drift is considered. It is assumed that the control vector fields together with their iterated Lie brackets satisfy Hormander's condition in a neighborhood of the origin. Then the problem of exponential stabilization is treated by exploiting periodic time-varying feedback controls. An explicit parametrization of such controllers is proposed under a suitable non-resonance assumption. It is shown that these controllers ensure the exponential stability of the closed-loop system provided that the period is small enough. The proposed control design methodology is applied for the stabilization of an underwater vehicle model and a front-wheel drive car.