Discrete Networked Dynamic Systems

Chapter 1: Mathematical background and examples

Abstract

In this chapter, we provide an overview of mathematical analysis followed by a brief overview of algebraic graph theory with emphasis on averaging and estimation algorithms defined over graphs. We also review basic concepts from matrix theory with a special emphasis on the so-called Perron–Frobenius theory. These concepts will be useful when analyzing the convergence of the linear dynamical systems discussed throughout the book. Next, we focus our attention on discrete-time networked dynamic systems (DNDSs), where the underlying connection topology couples the agents at their outputs. A distinction is made between DNDSs with homogeneous agent dynamics and NDSs with heterogeneous agent dynamics. ...