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Matrix-Weighted Graphs : Theory and Applications / by Minh Hoang Trinh, Hyo-Sung Ahn.
- Format:
- Book
- Author/Creator:
- Trinh, Minh Hoang.
- Series:
- Lecture Notes in Control and Information Sciences, 1610-7411 ; 498
- Language:
- English
- Subjects (All):
- System theory.
- Control theory.
- Graph theory.
- Automatic control.
- Robotics.
- Systems Theory, Control.
- Graph Theory.
- Control and Systems Theory.
- Complex Systems.
- Robotic Engineering.
- Local Subjects:
- Systems Theory, Control.
- Graph Theory.
- Control and Systems Theory.
- Complex Systems.
- Robotic Engineering.
- Robotics.
- Physical Description:
- 1 online resource (643 pages)
- Edition:
- 1st ed. 2026.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2026.
- Summary:
- This book presents and systematizes results in matrix-weighted graphs, a powerful tool for modeling and analysis of multi-dimensional networked systems. The authors select topics addressing fundamental issues, which they arrange in four parts: • graphs and networks with matrix weighting, showing how the matrix-weighted Laplacian forms the foundation for further theoretical developments; • development of algorithms for various purposes from the determination of connectivity to quantitative measurement as a key pillar in network design and analysis; • control-theoretic integration, providing a framework with the matrix-weighted consensus algorithm playing a central role and which coordinates interacting dynamical agents from each vertex in a cooperative and distributed manner; and • applications of matrix-weighted graphs in network synchronization, social networks, networked input–output economics, network localization and formation control. The theoretical results provide a firm foundation for researchers wishing to pursue the study of matrix-weighted networks and related topics and are accessible to graduate students with a background in engineering mathematics. Many of the definitions, analyses, and designs in this book are accompanied by figures, examples and numerical simulations. MATLAB® and Simulink® simulations to assist the reader in understanding and further developing such features are available for download.
- Contents:
- Part I: Graphs and Networks with Matrix-Weights
- Matrix-Weighted Graphs
- Matrix-Weighted Laplacian
- Physical Interpretation and Motivational Examples
- Part II: Algorithms
- Connectivity
- Spanning Trees
- Quantitative Measures
- Part III: Control
- Matrix-Weighted Consensus
- Discrete-Time and Randomized Algorithms
- Accelerated Algorithms
- Robustness
- Tracking
- Time-Delays
- Part IV: Applications
- Synchronization
- Scaling Matrices
- Networked Input–Output Analysis
- Bearing-Only Formation Control.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-032-03079-X
- 9783032030795
- OCLC:
- 1581075931
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