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Efficient numerical algorithms for balanced stochastic truncation [PDF]
, 2001 If \(G\) is the transfer function of a stable linear time-invariant system and suppose \(G(s)G^T(-s)=W^T(-s)W(s)\), then a reduced order model \(G_r\) can be obtained by truncating a balanced realization of \(G\). For balancing, one needs the controllability grammian \(P\) of \(G\) and the observability grammian \(Q\) of \(W\).
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Mixed Positive-Bounded Balanced Truncation
IEEE Transactions on Circuits and Systems II: Express Briefs, 2021Reducing the order of positive real and bounded real systems has received great interest over the years. Several methods have been published regarding these issues which are able to produce positive real or bounded real reduced models. However, none of them can guarantee that the reduced models are both positive real and bounded real at the same time ...
Zeinab Salehi +2 more
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On the Balanced Truncation of LTV Systems
IEEE Transactions on Automatic Control, 2006This note furthers results on the balanced truncation of stable linear time-varying discrete-time systems. The main result contributes better error bounds than the currently available ones in certain model reduction scenarios; this is demonstrated in an example of a four-mass translational system.
Farhood, Mazen, Dullerud, Geir E
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Generalized balanced stochastic truncation
29th IEEE Conference on Decision and Control, 1990A modification of the balanced stochastic truncation method for relative error model reduction is introduced. The method is shown to satisfy an infinity norm bound on the relative error between the full order and the reduced order models. The discrete time balanced stochastic truncation algorithm is at the heart of the new method, and a relative error ...
M. Green, B.D.O. Anderson
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Balanced truncation with spectral shaping for RLC interconnects
Proceedings of the ASP-DAC 2001. Asia and South Pacific Design Automation Conference 2001 (Cat. No.01EX455), 2001This paper presents a numerically stable and efficient algorithm for model reduction of large RLC networks using a frequency-weighted balanced truncation technique. The salient features of this algorithm include guaranteed stability of the reduced transfer function as well as availability of provable frequency-weighted error bounds.
Payam Heydari, Massoud Pedram
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An improved algorithm for frequency weighted balanced truncation
IEEE Conference on Decision and Control and European Control Conference, 2011In this paper, a new frequency weighted balanced truncation based on Lin and Chiu's technique [1] is presented. The method proposed is a modification to Sreeram and Sahlan's technique [2] by using the relationship between the intermediate reduced order model and the final reduced order model.
Wan Mariam Wan Muda +2 more
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Improved results on frequency weighted balanced truncation
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009In this paper, we present some new results on frequency weighted balanced truncation which is a significant improvement on Lin and Chiu's frequency weighted balanced truncation technique [7]. The reduced order models which are guaranteed to be stable in case of double-sided weighting, are obtained by direct truncation.
Victor Sreeram, Shafishuhaza Sahlan
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A Novel Scheme for Positive Real Balanced Truncation
2007 American Control Conference, 2007Here, model reduction, based on balanced truncation, of stable and passive systems will be considered. An overview over some of the already existing techniques will be given; Lyapunov balancing, Riccati balancing and Stochastic balancing. Subsequently a novel scheme for positive real balanced truncation will be proposed.
Kari Unneland +2 more
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Balanced stochastic truncation of coupled 3D interconnect
Proceedings of 2013 International Conference on IC Design & Technology (ICICDT), 2013Model order reduction techniques have been used extensively to reduce the complexity of extracted interconnect circuits and to expedite fast and accurate circuit simulation. In this paper, we introduce a balanced stochastic truncation in model order reduction of a coupled 3D interconnect to provide uniform approximation of the frequency response of the
Amir Zjajo +2 more
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On model reduction via empirical balanced truncation
Proceedings of the 2005, American Control Conference, 2005., 2005Empirical balanced truncation is considered as an approach for deriving reduced-order models of large-scale nonlinear systems that are of interest in the design of feedback control systems. Empirical balanced truncation is related to the widely-applied proper orthogonal decomposition (POD) methodology and yet may be better suited for closed-loop ...
Douglas A. Lawrence +2 more
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