Jan Lunze

Graph-Theoretical Methods
in Systems Theory and Control

Contents

The book is divided into three parts, which distinguish with respect to their graph-theoretical requirements. Within these parts, the graph-theoretical methods and their application to systems analysis and control design are separated by chapters:

• Part I: Graph and graph search
  
  Graph-theoretical methods:
  Graph search
  Reachability analysis
  Algorithm A*
  
  Applications:
  Graph search in logic-based knowledge processing: Inference graphs
  Graph-theoretical methods for approximate reasoning: ATMS graphs, Bayesian networks
  
  

• Part II - Algebraic graph theory

  
  Graph-theoretical methods:
  Graph properties analysed by means of the adjacency matrix
  Graph-theoretical interpretation of the determinant and the rank of a matrix
  
  Applications:
  Decomposition and aggregation of interconnected systems: coupling graphs
  Signal-flow graphs: Mason's formula
  Generic properties of linear systems: structure graphs
  Graph-theoretical modelling and analysis of electrical networks: circuit graphs
  General flow problem: flow networks
  Structural analysis of discrete-event systems: automaton graphs
  
  

• Part III - Bipartite graphs and random graphs

  
  Graph-theoretical methods:
  DM decomposition of bipartite graphs
  Properties of random graphs
  
  Applications:
  Structural analysis of constraint sets: bipartite structure graphs
  Networked control systems: communication graphs, random coupling graphs
  


Table of contents

Sample chapter