The Mathematics of Networks of Linear Systems

Paul A. Fuhrmann is Professor Emeritus in the Department of Mathematics at Ben-Gurion University of the Negev. His current research interests are in the following directions: Algebraic System Theory, control, observation and model reduction for networks of linear systems.

Introduction.-Rings and Modules of Polynomials.- Functional Models and Shift Spaces.- Linear Systems.- Tensor Products, Bezoutians and Stability.-State Feedback and Output Injection.-Observer Theory.- Nonnegative Matrices and Graph Theory.- Interconnected Systems.-Control of Standard Interconnections.- Synchronization and Consensus.- Control of Ensembles.- References.- Index.

lt;p>"In the voluminous book under review the authors illustrate their perspective on modelling and control of networks of linear finite-dimensional systems. ... This is an excellent book that can be appreciated both by readers familiar with the polynomial approach, and by readers unaccustomed to functional models. ... The historical sections at the end of each chapter are helpful because they explain the broader context and suggest further reading to both types of readers." (Paolo Rapisarda, Mathematical Reviews, March, 2016)