Certifying Set Attractivity for Discrete-Time Uncertain Nonlinear Switched Systems

TL;DR

This paper introduces AG-functions to certify set attractivity in uncertain nonlinear switched systems, providing a constructive method and practical examples including a biological system case study.

Contribution

It proposes a new class of functions, AG-functions, for certifying attractivity, and links their existence to control contractive sets in discrete-time uncertain nonlinear systems.

Findings

AG-functions guarantee robust local attractivity.

Constructive method for piecewise AG-functions based on contractive sets.

Application to a biological system model demonstrates practical relevance.

Abstract

We introduce a new class of functions, called Attractivity Guarantee (AG)-functions, to certify the attractivity of sets for uncertain nonlinear switched systems in discrete time. The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function, and hence the robust local attractivity of the set itself. We illustrate the proposed framework through examples that elucidate the theoretical concepts, and through the case study of a nonlinear switched system modelling antimicrobial resistance, which highlights the practical relevance of the approach to the analysis of biological systems.