Abstract
This paper investigates the large scale system consisting of a number of subsytems by using the theory of directed graphs. It is assumed that each subsystem is characterized by a canonical form of the state equation. The problem of characterizing the total system by the canonical form of the state equation which contains all the informations of the total system is discussed. Some sufficient conditions for the problem are derived by applying the adjacency matrices of the directed graphs.
It is shown that the large scale system consisting of the blocks characterized by the dual forms of the state equations and reversing the direction of every line of the block represented system could be characterized by the dual forms of the original state equations.
As an application of the presented theory a design procedure for dynamic compensators achieving the pole-assignment is presented. An example is included to show the procedure. It is shown that observing the design procedure using the state observer from the presented theory a new algorithm obtaining the dynamic controllers could be derived.
