Backstepping design for incremental stability

TL;DR

This paper introduces a backstepping control design method specifically for achieving incremental stability in nonlinear systems, addressing a gap where most existing methods focus on stability rather than incremental stability.

Contribution

The paper develops a novel backstepping approach tailored for incremental stability, expanding control design techniques beyond traditional stability to include incremental stability.

Findings

Successfully synthesized a controller for a synchronous generator

Demonstrated effectiveness of the method in achieving incremental stability

Extended backstepping design to nonlinear systems for incremental stability

Abstract

Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this paper, we develop a backstepping design approach for incremental stability. The effectiveness of the proposed method is illustrated by synthesizing a controller rendering a synchronous generator incrementally stable.