ON PURE STRUCTURE OF DYNAMIC SYSTEMS

Abstract

This chapter discusses the pure structure of dynamic systems. It discusses the relationship between dynamic systems, directed graphs, and interconnection matrices. Inputs, states, and outputs of a system are represented by input, state, and output points of the corresponding digraph. The lines of the digraph and the entries of the related interconnection matrix are determined in the usual way by occurrence of inputs, states, and outputs in the system equations. The chapter discusses the notion of input and output truncated digraphs and the use of the reachability and antecedent sets to define input and output reachability of dynamic systems. Using the path matrix, it develops an algebraic criterion for input and output reachability that can be applied to dynamic systems using effective algorithms already available in the digraph studies of computer systems. The chapter discusses the partitions and condensations of digraphs as related to dynamic systems, which provide an appropriate setting for analyzing the important reachability properties of large-scale systems composed of interconnected subsystems.