# Structured linear fractional parametric controller design with $\mathcal{H}_\infty$ performances

## TL;DR

This paper introduces a straightforward method for designing structured parametric controllers in linear fractional form using $H_infty$ optimization, enabling flexible controller construction with varying performance levels.

## Contribution

It presents an original approach to structured $H_infty$ optimization for parametric controller design, including practical and numerical considerations.

## Key findings

- Successfully designed a parametric controller for a parameter-dependent beam model.
- Developed a controller with parameter-dependent performance for a building model.
- Demonstrated the approach on complex academic examples.

## Abstract

This paper proposes an simple but yet effective approach to structured parametric controller design in a linear fractional form. The main contribution consists in using structured $\mathcal{H}_\infty$ oriented optimization tools in an original manner to either (i) construct a parametric controller or (ii) a family of controllers with varying performances. Practical and numerical issues are also discussed to provide readers and practitioners a simple way to deploy the proposed process. The overall approach is illustrated through two numerical academical (but still complex) examples illustrating two applications: first, a parametric controller design adapted to a parameter dependent model of a clamped beam and, second, a controller with parameter dependent performance applied on a building model.