Krasovskii's Passivity

TL;DR

This paper introduces Krasovskii's passivity, a new system property, along with conditions, classes of systems, and a control technique that extends traditional passivity-based control methods, demonstrated on electrical systems.

Contribution

The paper proposes Krasovskii's passivity, provides conditions for it, analyzes relevant system classes, and develops a new control method applicable when standard passivity control is challenging.

Findings

Krasovskii's passivity is a valid system property with practical conditions.

Certain port-Hamiltonian and gradient systems are Krasovskii's passive.

The new control technique is effective on electrical systems like Boost converters and RLC circuits.

Abstract

In this paper we introduce a new notion of passivity which we call Krasovskii's passivity and provide a sufficient condition for a system to be Krasovskii's passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii's passive. Moreover, we provide a new interconnection based control technique based on Krasovskii's passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit.