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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.
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