Krasovskii's Passivity

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

Passivity-Based Control

Stabilization of physical systems by shaping their energy function is a well-established technique whose roots date back to the work of Lagrange and Legendre. Potential energy shaping for fully actuated mechanical systems was first introduced in Takegaki and Arimoto (Trans ASME J Dyn Syst Meas Control 12:119--125, 1981) more than 30 years ago. In Ortega and Spong (Automatica 25(6):877--888, 1989) it was proved that passivity was the key property underlying the stabilization mechanism of these designs, and the, now widely popular, term of passivity-based control was coined. In this chapter we summarize the basic principles and some of the main developments of this controller design technique

Passivity-Based Control

Stabilization of physical systems by shaping their energy function is a well-established technique whose roots date back to the work of Lagrange and Legendre. Potential energy shaping for fully actuated mechanical systems was first introduced in Takegaki and Arimoto (Trans ASME J Dyn Syst Meas Control 12:119--125, 1981) more than 30 years ago. In Ortega and Spong (Automatica 25(6):877--888, 1989) it was proved that passivity was the key property underlying the stabilization mechanism of these designs, and the, now widely popular, term of passivity-based control was coined. In this chapter we summarize the basic principles and some of the main developments of this controller design technique

Discrete port-controlled Hamiltonian dynamics and average passivation

The paper discusses the modeling and control of port-controlled Hamiltonian dynamics in a pure discrete-time domain. The main result stands in a novel differential-difference representation of discrete port-controlled Hamiltonian systems using the discrete gradient. In these terms, a passive output map is exhibited as well as a passivity based damping controller underlying the natural involvement of discrete-time average passivity

Krasovskii and Shifted Passivity-Based Control

In this article, our objective is to develop novel passivity-based control techniques by introducing a new passivity concept named Krasovskii passivity. As a preliminary step, we investigate the properties of Krasovskii passive systems and establish relations among four relevant passivity concepts including Krasovskii passivity. Then, we develop novel dynamic controllers based on Krasovskii passivity and based on shifted passivity