Concept Of The Decomposition And Aggregation Method With Example: Part 1

Abstract

This paper describes the basic concept of the decomposition and aggregation method. It shows the feasibility of the method and its advantages when applied, particularly to large scale systems. This method is extensively used in solving problems related to control engineering, economics, optimization and stability. This paper also illustrates specifically the application of the method of decomposition and aggregation in the analysis of dynamic systems. It is divided into two important parts, namely; the decomposition part which involves breaking up a large system into subsystems and the aggregation part which is obtained through a reformulation of the Liapunov's second method (direct method). The relation between the decomposition and the aggregation methods is also shown. The procedure for checking the stability based on this concept is also outlined.For further illustration, an example of a dynamic system has been included. It shows how the system is decomposed and aggregated to suit the requirement for stability analysis.