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A survey of model reduction by balanced truncation and some new results. (English) Zbl 1061.93022

Summary: Balanced truncation is one of the most common model reduction schemes. In this note, we present a survey of balancing related model reduction methods and their corresponding error norms, and also introduce some new results. Five balancing methods are studied: (1) Lyapunov balancing, (2) stochastic balancing, (3) bounded real balancing, (4) positive real balancing and (5) frequency weighted balancing. For positive real balancing, we introduce a multiplicative-type error bound. Moreover, for a certain subclass of positive real systems, a modified positive-real balancing scheme with an absolute error bound is proposed. We also develop a new frequency-weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system Gramians. Two numerical examples are illustrated to verify the efficiency of the proposed methods.

MSC:

93B11 System structure simplification
93B17 Transformations
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
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