Reduction Principles and the Stabilization of Closed Sets for Passive Systems

TL;DR

This paper introduces reduction principles for passive systems that enable the stabilization of closed invariant sets using passivity-based feedback, providing conditions for asymptotic stability based on properties of invariant subsets.

Contribution

It presents novel reduction principles that allow stability analysis of passive systems by examining invariant subsets, advancing the understanding of stabilization techniques.

Findings

Reduction principles for passive systems are established.

Conditions for asymptotic stabilization of invariant sets are derived.

The approach simplifies stability analysis by focusing on invariant subsets.

Abstract

In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space.