Linear Matrix Inequalities in Control

Abstract

Objective Linear matrix inequalities (LMIs) have proven to be a powerful tool to approach control problems that appear hard, if not impossible, to solve in an analytic fashion. The history of LMIs goes back to the forties and their role in control became emphasized in the sixties (Kalman, Yakubovich, Popov, Willems). Contemporary numerical interior-point methods and semi-definite programming techniques are increasingly powerful and allow solving LMIs in a practically efficient manner (Nesterov, Nemirovskii 1994). Several Matlab software packages are available that allow a simple coding of general LMI problems that arise in typical control problems.