Graph-Theoretical Methods in Systems Theory and Control
Modelling, analysis and design methods based on directed graphs, bipartite graphs, and random graphs
Description
Many dynamical phenomena seem to be very complex, but have a relatively simple structural cause, which can be discovered by graph-theoretical methods. This textbook describes for numerous scenarios how to use the structural properties of a system to simplify modelling, analysis or design tasks. The readers learn to extract structure graphs from diverse information and to solve problems of systems and control theory in a graph-theoretical way.
The book explains numerous graph-theoretical representations of dynamical systems: Block diagrams for the decomposition of systems; Signal-flow graphs for the analysis of interconnected linear systems; Bayesian networks for dealing with probabilistic information; Inference graphs for knowledge-based problem solving; Automaton graphs for discrete-event systems; Circuit graphs for modelling electrical networks; Structure graphs to represent generic properties of linear systems; Flow networks for the analysis of transportation systems; Communication graphs of networked control systems; Bipartite graphs for fault diagnosis; Random coupling graphs to use the small-world property.
With 114 examples, 118 exercises and MATLAB scripts.
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