Generalized balanced and approximately balanced representations

(1992) Generalized balanced and approximately balanced representations. Masters thesis, King Fahd University of Petroleum and Minerals.

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Arabic Abstract

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English Abstract

This thesis consists of three main parts. In the first part, the conditions on the generalized Lyapunov matrix equations that are produced from poles clustering theorem is relaxed for controllable system. This result is used in balanced model reduction to produce a reduced order model with poles clustered in the same region as the poles of the full order model. In the second part, when bilinear transformation is used the controllability gramian of the system is equal to the generalized controllability gramian of the transformed system with respect to a given circle. This circle is determined from the bilinear transformation. Using bilinear transformation and the above theorem, a new balanced model reduction technique is developed. In this technique, the error frequency response is forced to be a high pass instead of low pass. In the third part, the complexity of a large scale system makes the computations of reduced order models based on balancing impractical. However, typically there is a weak coupling between the subsystems of a large scale system. This is used to derive approximate balanced-truncated reduced order models of a large scale discrete system with reliable and tractable computations. The condition for validity of the approximations and bounds on the norms of the approximation errors are also derived.

Item Type: Thesis (Masters)
Subjects: Electrical
Department: College of Engineering and Physics > Electrical Engineering
Committee Advisor: Al-Saggaf, U. M.
Committee Members: Bettayeb, Mammar and Bakhashwain, Jamil M. and Bakri, Talal M.
Depositing User: Mr. Admin Admin
Date Deposited: 22 Jun 2008 13:42
Last Modified: 01 Nov 2019 13:47
URI: https://eprints.kfupm.edu.sa/id/eprint/9505