  Perron-Frobenius theorem is a fundamental tool in matrix analysis that has
applications to complex networks, population dynamics, social learning, and
numerous physical, engineering, and economic phenomena. However, since this
theorem and many of its extensions can be applied only to a single matrix at a
time, their applications in networked dynamical systems are limited to static
networks. To extend the applicability of these results to time-varying
networks, we generalize two assertions of the Perron-Frobenius theorem to
sequences as well as continua of row-stochastic matrices. Our results have
potential applications in areas such as distributed averaging, optimization,
and estimation.
