Networked Control Systems: Convergence Rate and Digraphs

This lecture covers the analysis of the rate of convergence to consensus in networked control systems, focusing on consensus in digraphs that are not strongly connected. It discusses subgraphs, doubly stochastic matrices, and the essential spectral radius. Notable examples and the difficulty of computing Pess(A) are highlighted, along with the implications for consensus. The lecture also explores weight assignment problems and the main results related to consensus in different types of digraphs. Examples of complete graphs and opinion dynamics with globally reachable nodes are presented to illustrate the concepts.