In this monograph we consider the class of continuous-time positive switched systems. We
discuss several problems, including stability, performance analysis, stabilization via …

Ergodic optimization is the study of problems relating to maximizing orbits and invariant
measures, and maximum ergodic averages. An orbit of a dynamical system is called a larger …

Proceedings of the International Congress of Mathematicians (ICM 2018) : ERGODIC
OPTIMIZATION OF BIRKHOFF AVERAGES AND LYAPUNOV Page 1 P . I . C . M . – 2018 Rio …

Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which
states that the joint spectral radius is equal to the generalized spectral radius for a matrix …

The joint spectral radius of a compact set of d× d matrices is defined to be the maximum
possible exponential growth rate of products of matrices drawn from that set. In this article …

The pressure function P (A, s) plays a fundamental role in the calculation of the dimension of
“typical” self-affine sets, where A=(A 1,…, A k) is the family of linear mappings in the …

We introduce the notion of joint spectrum of a compact set of matrices S⊂ GL d (C), which is
a multi‐dimensional generalization of the joint spectral radius. We begin with a thorough …

The lower spectral radius, or joint spectral subradius, of a set of real matrices is defined to be
the smallest possible exponential growth rate of long products of matrices drawn from that …

In several papers of 2013–2016, Guglielmi and Protasov made a breakthrough in the
problem of the joint spectral radius computation, developing the invariant polytope algorithm …

We analyze the maximal growth of trajectories of discrete-time linear switching system, ie,
controlled linear systems with the control set being an arbitrary compact set of matrices. This …