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This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature.

Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either deterministic or randomized. The theory needed for a full understanding of the models is constructed without assuming any knowledge of Markov chains or Perron-Frobenius theory. Jointly with their analysis of the convergence of averaging dynamics, the authors derive the properties of stochastic matrices. These properties are related to the topological structure of the associated graph, which, in the book´s perspective, represents the communication between agents. Special attention is paid to how these properties scale as the network grows in size.

Finally, the understanding of stochastic matrices is applied to the study of other problems in multi-agent coordination: averaging with stubborn agents and estimation from relative measurements. The dynamics described in the book find application in the study of opinion dynamics in social networks, of information fusion in sensor networks, and of the collective motion of animal groups and teams of unmanned vehicles. Introduction to Averaging Dynamics over Networks will be of material interest to researchers in systems and control studying coordinated or distributed control, networked systems or multiagent systems and to graduate students pursuing courses in these areas.

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Graph Theory.- Averaging in Time-Invariant Networks.- Averaging in Time-Varying Networks.- Performance and Robustness of Averaging Algorithms.- Averaging with Exogenous Inputs and Electrical Networks.- Index.

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"This book gives a nice, conscientious introduction to the theory of averaging dynamics over networks. ... The book is essentially self-contained. In particular, it does not assume any knowledge of Perron-Frobenius theory, or Markov chain convergence. Every chapter of the book is complemented by numerous exercises and bibliographical notes." ( Jirì Cernì, Mathematical Reviews, February, 2019)

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