# On Passivity of Fractional Order Systems

## TL;DR

This paper extends the concepts of passivity and dissipativity to fractional order systems, demonstrating their stability, compositionality, and passivation through feedback control, supported by numerical examples.

## Contribution

It introduces generalized passivity definitions for fractional order systems and analyzes their stability, compositionality, and passivation methods, which were not previously well-understood.

## Key findings

- Passivity notions are successfully extended to fractional order systems.
- The stability and compositionality properties are analogous to integer order systems.
- Numerical examples validate the theoretical concepts.

## Abstract

We generalize notions of passivity and dissipativity to fractional order systems. Similar to integer order systems, we show that the proposed definitions generate analogous stability and compositionality properties for fractional order systems as well. We also study the problem of passivating a fractional order system through a feedback controller. Numerical examples are presented to illustrate the concepts.