Networked Control Systems: Graph Theory and Stochastic Matrices

This lecture covers the basics of networked control systems, focusing on graph theory and stochastic matrices. Topics include adjacency matrices, graph exploration, powers of adjacency matrices, averaging in wireless sensor networks, collective models, spectral properties of non-negative matrices, and the Perron-Frobenious theorem. The instructor discusses the dynamics captured by matrices with special properties, the analysis of consensus algorithms, and the localization of eigenvalues using Gershgorin disks. The lecture also addresses the spectral properties of row-stochastic matrices, the convergence of powers of stochastic matrices, and the properties of adjacency matrices through associated digraphs.