Model Reduction via Generalized Frequency Interval Cross Gramian  ⁎ ⁎This work is supported by Science and Engineering Research Board, Government of India under Overseas postdoctoral fellowship grant SB/SO/PDF-262/2015-16.

Kumar, Deepak; Sreeram, Victor

doi:10.1016/j.ifacol.2018.05.005

Cited by 4 publications

(1 citation statement)

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“…Similarly, if P(s) is unstable, the frequency-weighted cross-gramian cannot be computed for (A, B, C, D) even if P(s) is a SISO system. Inspired by References [22] and [23], we generalize the computation of frequency-weighted gramians for unstable systems. Let the state-space realizations of W o (s) and W o (s)P(s) be…”

Section: S)mentioning

confidence: 99%

Reduced Order Controller Design for Symmetric, Non-Symmetric and Unstable Systems Using Extended Cross-Gramian

et al. 2019

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In model order reduction and system theory, the cross-gramian is widely applicable. The cross-gramian based model order reduction techniques have the advantage over conventional balanced truncation that it is computationally less complex, while providing a unique relationship with the Hankel singular values of the original system at the same time. This basic property of cross-gramian holds true for all symmetric systems. However, for non-square and non-symmetric dynamical systems, the standard cross-gramian does not satisfy this property. Hence, alternate approaches need to be developed for its evaluation. In this paper, a generalized frequency-weighted cross-gramian-based controller reduction algorithm is presented, which is applicable to both symmetric and non-symmetric systems. The proposed algorithm is also applicable to unstable systems even if they have poles of opposite polarities and equal magnitudes. The proposed technique produces an accurate approximation of the reduced order model in the desired frequency region with a reduced computational effort. A lower order controller can be designed using the proposed technique, which ensures closed-loop stability and performance with the original full order plant. Numerical examples provide evidence of the efficacy of the proposed technique.

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Section: S)mentioning

confidence: 99%