This paper reviews the vast literature on static output feedback design for linear time-
invariant systems including classical results and recent developments. In particular, we …

The affine rank minimization problem consists of finding a matrix of minimum rank that
satisfies a given system of linear equality constraints. Such problems have appeared in the …

Convex Analysis is the calculus of inequalities while Convex Optimization is its application.
Analysis is inherently the domain of the mathematician while Optimization belongs to the …

Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with
many important applications in machine learning and statistics. In this paper we propose a …

In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a
convex set. The rank minimization problem (RMP) arises in diverse areas such as control …

The idea of a finite collection of closed sets having “linearly regular intersection” at a point is
crucial in variational analysis. This central theoretical condition also has striking algorithmic …

We prove that if two smooth manifolds intersect transversally, then the method of alternating
projections converges locally at a linear rate. We bound the speed of convergence in terms …

Algorithms to construct/recover low-rank matrices satisfying a set of linear equality
constraints have important applications in many signal processing contexts. Recently …

This paper presents a Newton-like algorithm for solving systems of rank constrained linear
matrix inequalities. Though local quadratic convergence of the algorithm is not a priori …

This paper addresses the problem of static output feedback synthesis and focuses on H 2
optimisation. The bilinear problem of finding a control feedback gain K and a Lyapunov …