A review of the results on consensus models in asynchronous multi-agent systems with discrete and continuous time is presented. The description of mathematical methods developed in recent years, which are used in the analysis of problems of stability, stabilization and consensus for linear multi-agent systems with discrete time, is given. The basis of these methods is the idea of ​​using the notion of joint / generalized spectral radius of matrix sets for analyzing the rate of convergence of matrix products with factors from matrix sets with special properties.