LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations

The information in this chapter is referenced from: "Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization" by Benjamin Recht, Maryam Fazel, and Pablo A. Parrilo, published in SIAM Review 2010, Volume 52, Issue 3, pages 471-501.

Contents

• Rank minimization problem: general form

• Minimum-Order Linear System Realization via minimizing the rank of the Hankel matrix

• Low-Rank Matrix Completion

• Low-Dimensional Euclidean Embedding Problem

• Nuclear Norm Minimization

• Nuclear Norm Minimization

• Low-Rank Parametrization