Synchronization and Convergence of Linear Dynamics in Random Directed Networks

Recently, methods in stochastic control are used to study the synchronization properties of a nonautonomous discrete-time linear system x(k+1) = G(k)x(k) where the matrices G(k) are derived from a random graph process. The purpose of this paper is to extend this analysis to directed graphs and more general random graph processes. Rather than using Lyapunov type methods, we use results from the theory of inhomogeneous Markov chains in our analysis. Sufficient conditions are derived that depend on the types of graphs that have nonvanishing probabilities. For instance, if a scrambling graph occurs with nonzero probability, then the system synchronizes.

By: Chai Wah Wu

Published in: RC23725 in 2005


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