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

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.