It is now widely recognized that a wide variety of problems arising in systems and control theory can be cast into convex feasibility/optimization problems represented by linear matrix inequalities (LMIs). Since efficient and reliable interior-point algorithms have been provided in the late 1980's, numerous control problems have found a tractable solution within the LMI framework. On the other hand, the development of LMI techniques opens up a new horizon in control theory and poses particularly novel problems to be solved. Most of them remain open and investigated intensively by many researchers in the world.  

In addition to being a powerful 'numerical' tool for control problems, LMIs should be helpful also to interpret existing results in a concise way and find out completely novel results in 'analytic' form. In particular, once we have reduced control problems at hand into convex problems in terms of LMIs, we can readily consider its dual problems that, in most cases, provide new insights to the problems considered.   

The problems around LMIs are surely widespread. For further developments of LMIs in control, interdisciplinary research efforts from various fields would be desired.  

The main goal for opening this web page is to provide useful informations to the researchers who are interested in LMIs. This web page tries to dispatch up-to-date informations so that the research activities in the field become yet more lively.  Any comments and suggestions to improve the web page are welcome. Please contact Yoshio Ebihara or Dimitri Peaucelle.