The Joint Spectral Radius ─ Theory and Applications

The first part of this monograph is dedicated to theoretical results. The first two chapters present the above mentioned survey on the joint spectral radius. Its minimum growth counterpart, the joint spectral subradius, is also considered. The next two chapters point out two specific theoretical topics, that are important in practical applications: the particular case of nonnegative matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius. The author first presents the continuity of wavelet. He then studies the problem of the capacity of codes submitted to forbidden difference constraints. The notion of overlap-free words is then discussed, a problem that arises in combinatorics on words. The book then ends with the problem of trackability of sensor networks, and shows how the theoretical results developed in the first part allow to solve this problem efficiently.