Equilibrium-Independent Dissipativity with Quadratic Supply Rates

TL;DR

This paper explores equilibrium-independent dissipativity with quadratic supply rates in nonlinear control-affine systems, providing algebraic characterizations and stability results for both continuous and discrete-time cases, with applications to physical systems and optimization algorithms.

Contribution

It offers a novel algebraic characterization of EID with quadratic supply rates, extending Hill-Moylan lemma to a broader class of systems and time domains.

Findings

Characterization of EID via algebraic conditions similar to Hill-Moylan lemma

Results on internal, feedback, and absolute stability of EID systems

Illustrations with physical systems and convex optimization algorithms

Abstract

Equilibrium-independent dissipativity (EID) is a recently introduced system property which requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic supply rates for a common class of nonlinear control-affine systems. We provide an algebraic characterization of EID for such systems in the spirit of the Hill-Moylan lemma, where the usual stability condition is replaced by an incremental stability condition. Based on this characterization, we state results concerning internal stability, feedback stability, and absolute stability of EID systems. Finally, we study EID for discrete-time systems, providing the relevant definitions and an analogous Hill-Moylan-type characterization. Results for both continuous-time and discrete-time systems are illustrated through examples on physical systems and convex optimization algorithms.