Model reduction for state-space symmetric systems |
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Authors: | W.Q. Liu V. Sreeram K.L. Teo |
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Affiliation: | aDepartment of Electrical and Electronic Engineering, The University of Western Australia, Nedlands, W.A. 6907, Australia;bSchool of Mathematics and Statistics, Curtin University of Technology, Perth, W.A. 6001, Australia |
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Abstract: | In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions. |
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Keywords: | Model reduction Hankel singular values State-space symmetric systems |
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