Some classes of linear asynchronous multi-agent systems with discrete time are described for which the stability problem allows a constructive solution. Also described is a general analytical approach to the construction of numerical characteristics similar to the generalized spectral radius in the theory of stability, which would provide an opportunity to analyze the stabilizability of controlled multiagent systems. The work completes the review of the authors >, the first two parts of which are published in numbers 4, 5 for 2019.