Output contraction analysis of nonlinear systems

TL;DR

This paper introduces output contraction for nonlinear systems, linking it to exponential stability, and provides conditions for achieving it, with applications to time-invariant systems.

Contribution

It extends contraction theory to output contraction for nonlinear systems, establishing new stability criteria and connecting it to exponential stability analysis.

Findings

Output contraction generalizes existing contraction concepts.

A Lyapunov-based condition for output contraction is derived.

Application to nonlinear time-invariant systems demonstrates practical relevance.

Abstract

This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each other exponentially. This concept exhibits a more expansive nature when contrasted with another generalized contraction framework known as partial contraction. The first result establishes a connection between the output contraction of a time-varying system and the output exponential stability of its variational system. Subsequently, we derive a sufficient condition for achieving output contraction in time-varying systems by applying the output contraction Lyapunov criterion. Finally, we apply the results to analyze the output exponential stability of nonlinear time-invariant systems.