Necessity and Analysis of Model order Reduction Techniques

Abstract

There is a large number of techniques available for deriving reduced order models and lower order controllers. In this paper, the features and analysis of Frobenius Hankel (F H) norm, H2 norm and H∞ norm reduced order approximations is given. Also The necessary and sufficient conditions  for the  existence of an approximate solution within  a specified error γ will be found, these conditions  are given in terms  of a set of linear matrix  inequalities (LMI)  and  a matrix  rank  constraint for both  continuous  and  discrete  time  multi input-multi output systems.

In this paper we will introduce some of the popular methods to reduce the complexity of models, which depends mainly on the balanced state space representation and the Hankel singular values. These methods are balanced truncation and Hankel norm reduction methods.