General-Purpose LMI solvers with benchmarks

This paper presents the software package LMI-LAB for the manipulation and resolution of linear matrix inequalities (LMI). Fairly general systems of LMI´s can be handled as well as two important optimization problems under LMI constraints. The polynomial-time projectile method of Nesterov and Nemirovsky is used to solve the underlying convex optimization programs. Several benchmark examples demonstrate that the complexity and running time of these algorithms are by no means prohibitive. This confirms that LMI formulations constitute a computationally viable and reasonable approach to control system design