The Mathematics of Networks of Linear Systems

Description

This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area. Front Matter....Pages i-xiv Introduction....Pages 1-20 Front Matter....Pages 21-21 Rings and Modules of Polynomials....Pages 23-83 Functional Models and Shift Spaces....Pages 85-140 Linear Systems....Pages 141-206 Front Matter....Pages 207-207 Tensor Products, Bezoutians, and Stability....Pages 209-279 State Feedback and Output Injection....Pages 281-353 Observer Theory ....Pages 355-408 Front Matter....Pages 409-409 Nonnegative Matrices and Graph Theory....Pages 411-466 Interconnected Systems....Pages 467-505 Control of Standard Interconnections....Pages 507-552 Synchronization and Consensus....Pages 553-600 Control of Ensembles....Pages 601-644 Back Matter....Pages 645-662