Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

Many large-scale systems have inherent structures that can be exploited to facilitate their
analysis and design. This thesis investigates how chordal graph properties can be used to …

Optimization over non-negative polynomials is fundamental for nonlinear systems analysis
and control. This work investigates the relation between three tractable relaxations for …

A method to design plug-and-play (PnP) distributed controllers for large-scale nonlinear
systems represented by interconnected Takagi–Sugeno fuzzy models with nonlinear …

We consider the problem of designing a stabilizing and optimal static controller with a pre-
specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort …

In this note, we describe sufficient conditions when block-diagonal solutions to Lyapunov
and H∞ Riccati inequalities exist. In order to derive our results, we define a new type of …

We propose a distributed design method for decentralized control by exploiting the
underlying sparsity properties of the problem. Our method is based on the chordal …

Semidefinite programs (SDPs) are standard convex problems that are frequently found in
control and optimization applications. Interior-point methods can solve SDPs in polynomial …

This paper introduces a notion of decomposition and completion of sum-of-squares (SOS)
matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can …

In this paper, we introduce a set of block factor-width-two matrices, which is a generalisation
of factor-width-two matrices and is a subset of positive semidefinite matrices. The set of block …