Stabilization and state trajectory tracking problem for nonlinear control systems in the presence of disturbances

TL;DR

This paper addresses the stabilization and trajectory tracking of nonlinear control systems affected by disturbances, providing conditions for designing smooth state feedback controllers.

Contribution

It introduces sufficient conditions for the existence of smooth feedback controllers for nonlinear systems with disturbances.

Findings

Conditions for $C^k$ state feedback controller existence

Methodology for designing controllers in disturbed nonlinear systems

Framework applicable to a wide class of nonlinear control problems

Abstract

In this paper we consider the problem of stabilization and tracking of desired state trajectory for a wide range of nonlinear control problems with disturbances. We present the sufficient conditions for the existence of $C^k$ state feedback controllers and the process of their mathematical designing is described.