# Jan Lunze

# Graph-Theoretical
Methods

in Systems Theory and Control

## Modelling, analysis
and design methods

based on directed graph, bipartite graphs, and random graphs

1st edition 2024, XXVII, 765 pp.

With 516 figures, 115 examples, 117 exercises and MATLAB scrips

Edition** M**o**R**a

ISBN 9789403726854

has appeared on January 21, 2024

Many dynamical phenomena seem to be very complex, but have a simple structural cause, which can be discovered by graph-theoretical means. 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 about a system and to solve problems of systems and control theory in a graph-theoretical way.

Numerous graph-theoretical representations of dynamical systems have been developed for different analysis and design problems:

**Block diagrams and coupling graphs**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 the analysis of discrete-event systems**Circuit graphs**for modelling electrical networks**Structure graphs**for the analysis of generic properties of linear systems**Flow networks**for the representation of flow and transportation systems**Communication graphs**for the design of networked control systems**Bipartite structure graphs**for the decomposition of linear constraint sets**Bipartite graphs**for fault diagnosis**Random coupling graphs**to use the small-world property of large systems

**Additional information**

Flyer