Matrosov's theorem using a family of auxiliary functions: an analysis tool to aid time-varying nonlinear control design

TL;DR

This paper introduces a generalized Matrosov's theorem with auxiliary functions to analyze the stability of nonlinear time-varying systems, enhancing control design methods for complex interconnected systems.

Contribution

The paper extends Matrosov's theorem using auxiliary functions, providing a new tool for stability analysis in nonlinear time-varying control systems.

Findings

The theorem guarantees uniform attractivity of the origin in nonlinear time-varying systems.

Application to port interconnected driftless systems demonstrates practical utility.

Addresses control of chained-form nonholonomic systems as a special case.

Abstract

We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskii-LaSalle invariance principle to the case of general nonlinear time-varying systems. We show the utility of our theorem by addressing a control problem of port interconnected driftless systems. The latter includes as special case, the control of chained-form nonholonomic systems which has been extensively studied in the literature.