Theory: Graphs and Matrices, properties of the Laplacian matrix and relation with graph connectivity. Non-negative matrices. Graphs and Dynamic Systems, Input and Output Reachability, Structural Controllability and Observability, Distributed Feedback Structures, Connective Stability and Stabilization, Vector Lyapunov Functions, Distributed Suboptimal and Optimal Control, Decentralized Observers and Feedback, Output Feedback Applications: a) Control of Smart Grids: Frequency Regulation with variable resources, Charging Control for Plug-in electric Vehicle, Wide Area Damping Control b) Cooperative Control of Multi-agent systems: Connectivity, Coordination and Consensus algorithms: Formation Control, Flocking, rendezvous. Adversarial interactions, Task assignment and routing
R. B. Bapat, Graphs and Matrices, TRIM Series, Hindustan Book Agency, 2011
C. Godsil and G. Royle, Algebraic Graph Theory, Springer, New York, 2001 (Available in Indian edition)
Dragoslav D. Siljak, Decentralized Control of Complex Systems, Mathematics in Science and Engineering vol 184, Academic Press, London, 1991
Aranya Chakraborty and Marija D. Ilic Editors, Control and Optimization Methods for Electric Smart Grids, Springer New York, 2012.
Jeff S. Shamma Editor, Cooperative Control of Distributed Multi-Agent Systems, John Wiley and Sons, West Sussex, England, 2007.