# On the SPRification of linear descriptor systems via output feedback

## TL;DR

This paper investigates conditions under which linear descriptor systems can be transformed into strictly positive real systems using output feedback, providing theoretical criteria and a controller synthesis method.

## Contribution

It offers a comprehensive set of conditions and a synthesis procedure for making descriptor systems SPR via output feedback, filling a gap in control theory.

## Key findings

- Derived time and frequency domain conditions for SPRification.
- Provided a controller design synthesis procedure.
- Validated results with illustrative examples.

## Abstract

We consider input-output systems in descriptor form and ask when such systems can be rendered SPR (strictly positive real) via output feedback. Time and frequency domain conditions are given to determine when and how this is possible. In addition, a synthesis procedure for controller design is also derived. Together, the results provide a complete answer to when a linear descriptor system can be made SPR via output feedback, and give a recipe for design of the feedback controller when it exists. Simple examples are given to illustrate our results and to demonstrate their efficacy.