Introduction

Abstract

The joint spectral radius characterizes the maximal asymptotic growth rate of a point submitted to a switching linear system in discrete time. In the last decades it has been the subject of intense research due to its role in the study of wavelets, switching systems, approximation algorithms, curve design, and many other topics. In parallel with these practical engineering applications, beautiful theoretical challenges have arisen in the effort to understand the joint spectral radius. These two facts make the study of the joint spectral radius a dream of a subject for a Ph.D. thesis, but perhaps a not so easy task.