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 projective method of Nesterov & Nemirovsky is used to solve the underlying convex optimization pro,grams. Several benchmark examples demonstrate that the complexity and running time of these algorithms are by no means prohibitive. This confirnis that LMI formulations constitute a computationally viable and reasonable approach to control system design.