This tutorial is about new system analysis techniques that were developed in the past few
years based on the sum of squares decomposition. We present stability and robust stability …

Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

This book provides an introduction to the analysis and control of linear parametervarying
systems, time-delay systems, and their interactions. The purpose is to give the readers some …

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI)
whose optimal solution can be characterized exactly. This family corresponds to the case …

A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions
reducible to a finite number of polynomial equalities and inequalities, it is shown how to …

We consider the problem of minimizing a polynomial over a semialgebraic set defined by
polynomial equations and inequalities, which is NP-hard in general. Hierarchies of …

SOSTOOLS is a MATLAB toolbox for constructing and solving sum of squares programs. It
can be used in combination with semidefinite programming software, such as SeDuMi, to …

This paper is concerned with polynomial optimization problems. We show how to exploit
term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of …

This monograph is based on the Ph. D. Thesis of the author [58]. Its goal is twofold: First, it
presents most researchwork that has been done during his Ph. D., or at least the part of the …

At the core of many sensing and imaging applications, the signal of interest can be modeled
as a linear superposition of translated or modulated versions of some template [eg, a point …