Networked Control Systems: Consensus Algorithms in Digraphs

This lecture by the instructor covers consensus algorithms in digraphs, focusing on the case where the digraph is not strongly connected. The main result from previous lectures is discussed, emphasizing the consensus algorithm's behavior with primitive and stochastic matrices. The lecture explores scenarios where the digraph is not strongly connected, providing examples like opinion dynamics with a single globally reachable node. The concept of powers of adjacency matrices is introduced, along with discussions on reducible digraphs and induced subgraphs. The lecture concludes with a proof regarding strongly connected components and globally reachable nodes in digraphs.