Contraction based stabilization of nonlinear singularly perturbed systems and application to high gain feedback

TL;DR

This paper introduces a contraction theory-based framework for stabilizing nonlinear singularly perturbed systems, enabling bounded tracking error without traditional Lyapunov constraints and extending applicability to a broader class of systems.

Contribution

It proposes a novel contraction-based stabilization method that relaxes Lyapunov conditions and is effective for both standard and non-standard singularly perturbed systems.

Findings

Achieves bounded tracking error with a contraction-based controller.

Removes the need for interconnection conditions in controller design.

Ensures stability bounds independent of perturbation parameter smallness.

Abstract

Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for stabilization of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard and non-standard singularly perturbed systems. This framework provides relaxation over traditional quadratic Lyapunov based method as there is no need to satisfy interconnection conditions during controller design algorithm. Moreover, the stability bound does not depend on smallness of singularly perturbed parameter. Combined with high gain scaling, the proposed technique is shown to assure contraction of approximate feedback linearizable systems. These findings extend the class of nonlinear systems which can be made contracting.