## Section: Application Domains

### Introduction

The bottom line of the team's activity is two-fold, namely function theory and optimization in the frequency domain on the one hand, and the control of certain systems governed by differential equations on the other hand. Therefore one can distinguish between two main families of applications: one dealing with the design and identification of diffusive and resonant systems (these are inverse problems), and one dealing with the control of certain mechanical systems. For applications of the first type, approximation techniques as described in section 3.1.1 allow one to deconvolve linear equations, analyticity being the result of either the use of Fourier transforms or the harmonic character of the equation itself. Applications of the second type mostly concern the control of systems that are “poorly” controllable, for instance low thrust satellites. We describe all these below in more detail.