About

I mainly have two research themes.

 

The first one stems from my PhD and consists in the study of the stability of linear periodic systems, coming from 1-D hyperbolic PDEs or delay systems, with a frequency method. Moreover, I give a mathematical justification of the use of the harmonic transfer function in electrical engineering to tackle the stability question of electronic amplifiers.

 

My second research subject is the exact controllability of linear time-invariant 1-D hyperbolic PDEs or delay equations. Unlike the classic methods used to treat these subjects, i.e. backstepping methods or observability inequalities, my work is based on algrebraic methods (convolution algebras) like R. Kalman and Y. Yamamoto, expressing the exact controllability in terms of a Bézout identity over Radon measures. In particular, the exact controllability amounts to the resolution of a corona problem.