Characterizing nonlinear systems with mixed input-output properties through dissipation inequalities

TL;DR

This paper introduces a constructive dissipativity-based method to characterize nonlinear systems with mixed input-output properties, enabling stability analysis of complex feedback systems beyond classical criteria.

Contribution

It provides a novel framework using specialized supply rates inspired by the generalized KYP lemma to identify mixed properties in nonlinear systems.

Findings

System characterization via dissipativity with specialized supply rates

Assessment of feedback stability beyond small-gain and passivity theorems

Applicability demonstrated through diverse examples

Abstract

Systems that show different characteristics, such as finite-gain and passivity, depending on the nature of the inputs, are said to possess mixed input-output properties. In this paper, we provide a constructive method for characterizing mixed input-output properties of nonlinear systems using a dissipativity framework. Our results take inspiration from the generalized Kalman-Yakubovich-Popov lemma, and show that a system is mixed if it is dissipative with respect to highly specialized supply rates. The mixed input-output characterization is used for assessing stability of feedback interconnections in which the feedback components violate conditions of classical results such as the small-gain and passivity theorem. We showcase applicability of our results through various examples.