Model reduction analysis using Hankel Norm Approximation on discrete-time linear system with the special shape of matrix A

Abstract

A system can describe real problems that occur in the environment. The system is the result of modeling of real problems. Based on the results of real problem modeling, it often produces a linear system with a special shape of matrix A. In general, to represent the actual conditions of the real problem accurately, a system with a large order is required. While on the other hand, in terms of analysis and computation of the system, it is not desired to have a system with a large order. Therefore, we propose to use a model reduction that produces a system with small orders but without significant errors. One of the commonly used model reduction methods is Hankel Norm Approximation (HNA). In this research, we analyze the process of model reduction with the HNA method in the discrete-time linear system which has special forms of the matrix A. The process of reduction of this model begins with the formulation of the initial system with a special shaped matrix A. Next, we analyze the nature of stability, controllability and observability of the initial system. Then a balanced system is formed and followed by model reduction using HNA. Based on the results of the model reduction simulation using HNA, it was found that the reduced system with HNA has the same performance and properties as the initial system, which is stable, controllable, and observable. Besides that, HNA model reduction is suitable for use at high frequencies and has a fast computation time.