How to solve three fundamental linear matrix inequalities in the löwner partial ordering

Abstract

This paper shows how to derive analytical solutions of the three fundamental linear matrix inequalities AXB ≥ C(> C, ≤ C, < C), AXA* ≥ B(> B, ≤ B, < B), AX +(AX)* ≥ B(> B, ≤ B, ≤ B) in the Löwner partial ordering by using ranks, inertias and generalized inverses of matrices. © Zagreb Paper JMI-08-01.