Error bounds in the gap metric for dissipative balanced approximations

Guiver, Christopher; Opmeer, Mark R.

doi:10.1016/j.laa.2013.09.032

Cited by 23 publications

(30 citation statements)

References 39 publications

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“…In response, balanced truncation has been extended to bounded real and positive real systems in [9] and [37], respectively, and to the infinite-dimensional case in [22]. Here the truncations do retain the respective dissipativity property and error bounds have also been established see, for example, [18] and [23]. We note that there is a false bound in [5], see [21].…”

Section: Chris Guivermentioning

confidence: 99%

The generalised singular perturbation approximation for bounded real and positive real control systems

Guiver

2019

Mathematical Control &Amp; Related Fields

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The generalised singular perturbation approximation (GSPA) is considered as a model reduction scheme for bounded real and positive real linear control systems. The GSPA is a state-space approach to truncation with the defining property that the transfer function of the approximation interpolates the original transfer function at a prescribed point in the closed right half complex plane. Both familiar balanced truncation and singular perturbation approximation are known to be special cases of the GSPA, interpolating at infinity and at zero, respectively. Suitably modified, we show that the GSPA preserves classical dissipativity properties of the truncations, and existing a priori error bounds for these balanced truncation schemes are satisfied as well.

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Section: Chris Guivermentioning

confidence: 99%

The generalised singular perturbation approximation for bounded real and positive real control systems

Guiver

2019

Mathematical Control &Amp; Related Fields

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“…Note that Σ i is obtained from positive real balancing of Σ i , and generally, there does not exist an a priori bound on Σ i −Σ i H∞ . Nevertheless, a posteriori bound can be obtained, see [10].…”

Section: Error Analysismentioning

confidence: 99%

Balanced truncation of networked linear passive systems

2019

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This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example. (Xiaodong Cheng), j.m.a.scherpen@rug.nl (Jacquelien M.A. Scherpen), b.besselink@rug.nl (Bart Besselink).

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“…Further, an a priori gap metric error bound together with an a posteriori H ∞ -error bound for positive real balanced truncation are established in [17]. Since we perform positive real balanced truncation, its transfer functionG(s) := B T sI 2r −Ã −1B is also positive real.…”

Section: Positive Real Balanced Truncationmentioning

confidence: 99%

“…Since we perform positive real balanced truncation, its transfer functionG(s) := B T sI 2r −Ã −1B is also positive real. Further, an a priori gap metric error bound together with an a posteriori H ∞ -error bound for positive real balanced truncation are established in [17].…”

Section: Positive Real Balanced Truncationmentioning

confidence: 99%