On input-to-state stability verification of identified models obtained by Koopman operator

TL;DR

This paper introduces a method using Koopman operator-based basis functions to verify input-to-state stability of identified models, with linear matrix inequality conditions and extensions for flexibility, supported by numerical examples.

Contribution

It presents a novel approach for input-to-state stability verification of models derived via Koopman operator, including relaxations for basis function restrictions.

Findings

The proposed conditions are expressed as linear matrix inequalities.

Extensions improve the flexibility of basis function selection.

Numerical examples demonstrate the effectiveness of the method.

Abstract

This paper proposes a class of basis functions for realizing the input-to-state stability verification of identified models obtained from the true system (assumed to be input-to-state stable) using the Koopman operator. The formulated input-to-state stability conditions are in the form of linear matrix inequalities. Two extensions are presented to relax the imposed restrictions on the basis functions. Several numerical examples are provided to demonstrate the efficacy of the proposed results.