My main scientific interests :My research interests lie in rational H2 approximation, parametrization issues for lossless functions and filter design.
My interest for lossless matrices is motivated by two main applications in system theory:
The main outcomes of my research are:
- Lossless matrices appear as cornerstone in matrix rational L2 approximation with stability constraint,
- The transfer functions of conservative systems, and in particular scattering matrices of frequency filters, are lossless.
- A powerful rational approximation algorithm, implemented in the software RARL2;
- A well-understood correspondence between the tangential Schur algorithm and balanced realizations which provides useful parametrizations;
- Original methods, based on Schur analysis, to deal with modeling, identification and design issues for filters and multiplexers.
Identification of microwave filters by analytic and rational H2 approximation
M. Olivi, F. Seyfert and J.P. Marmorat
Automatica 49(2013) 317-325 , doi: 10.1016/j.automatica.2012.10.005.
Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm
B. Hanzon, M. Olivi and R.L.M. Peeters
Linear Algebra and its Applications, 418 (2006), 793-820
Matrix rational H2 approximation: a gradient algorithm based on Schur analysis
P. Fulcheri and M. Olivi
SIAM Journal on Control and Optimization Vol. 36, No. 6, 2103-2127(1998)
The software RARL2
Teatching: Fourier Analysis (in french)
Popularization of science (in french)