I am trying to explore the mathematical domains of convex optimization, real algebraic geometry, functional analysis and dynamical systems. I would like to unveil existing links between these disciplines, and exploit them to study classical problems of systems control theory from a different perspective.
My background is in systems control engineering, following up the work of the Prague school on polynomial methods for systems control (Vladimir Kucera, mid 1970s) and the Toulouse school on convex optimization for systems control (Jacques Bernussou, mid 1980s). I am working at LAAS, a laboratory of CNRS founded in 1967 by Jean Lagasse to study systems control problems for the aerospace industry (now research activities at LAAS also include computer science, robotics, micro and nano-electronics). Historically, LAAS was created as an outgrowth of the electrical engineering laboratories of Toulouse whose history can be traced back to the Electrotechnical Institute of Toulouse created by Charles Camichel in 1907. See this document (in French) for more information on my French scientific genealogy. I have also a part-time affiliation with the Departement of Control Engineering, Faculty of Electrical Engineering of the Czech Technical University in Prague, an engineering school founded in 1707 by the Austrian Emperor Joseph I. See this document (in Czech) for an history of control engineering in this university. See also Vladimir Kucera's webpage in Czech or in English for more information on my Czech scientific genealogy.
Keywords: systems control, convex optimization over linear matrix inequalities (LMI), semidefinite programming (SDP), numerical algorithms for polynomial matrices.
AMS 2010 MSC: 93 (systems theory; control), 90C (mathematical programming).