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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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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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PABTEC: Passivity-Preserving Balanced Truncation for Electrical Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2010We present a passivity-preserving balanced truncation model reduction method for differential-algebraic equations arising in circuit simulation. This method is based on balancing the solutions of projected Lur'e equations. By making use of the special structure of circuit equations, we can reduce the numerical effort for balanced truncation ...
Reis, Timo, Stykel, Tatjana
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Extended balanced truncation for continuous time LTI systems
2018 European Control Conference (ECC), 2018In this paper we develop a continuous time counterpart of the balancing approach based on the extended Gramians for discrete time LTI systems. The extended Gramians are solutions to LMI's and can be seen as an extension/generalization of generalized Gramians which are solutions of the standard Lyapunov inequalities.
Scherpen, Jacquelien M.A. +1 more
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Equalization of loudspeaker response using balanced model truncation
The Journal of the Acoustical Society of America, 2015Traditional loudspeaker equalization algorithms cannot decide the order of an equalizer before the whole equalization procedure has been completed. Designers have to try many times before they determine a proper order of the equalization filter.
Xiansheng, Li +3 more
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Relative-error bound for discrete balanced stochastic truncation
International Journal of Control, 1990Fundamental differences between discrete-time balanced stochastic truncation (BST) and its continuous-time counterpart are shown to preclude a straightforward application of bilinear mappings for directly generalizing existing continuous-time error bounds.
Weizheng Wang, Michael G. Safonov
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Modified balanced truncation preserving ellipsoidal cone-invariance
53rd IEEE Conference on Decision and Control, 2014We consider model order reduction of stable linear systems which leave ellipsoidal cones invariant. We show how balanced truncation can be modified to preserve cone-invariance. Additionally, this implies a method to perform external positivity preserving model reduction for a large class of systems.
Christian Grussler, Anders Rantzer
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Generalized incremental balanced truncation for nonlinear systems
52nd IEEE Conference on Decision and Control, 2013The method of generalized incremental balanced truncation is introduced in this paper, providing a technique for model reduction of nonlinear systems in which the autonomous part of the vector field is anti-symmetric. This approach differs from existing balancing-like reduction techniques in the definition of two novel, incremental energy functions ...
Besselink, B. +3 more
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A note on closed-loop balanced truncation
Proceedings of 1995 34th IEEE Conference on Decision and Control, 1996The closed-loop balanced truncation (CLBT) is discussed. CLBT performs truncation on a realization of the controller in which the parts \(P_c\) and \(Q_c\) of the controllability and observability gramians that correspond to the controller states are balanced; as a result the closed-loop transfer function is changed as little as possible.
Schelfhout, Geert, De Moor, Bart
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Application of Balanced Truncation to Nonlinear Systems
Industrial & Engineering Chemistry Research, 2011The balanced truncation method for reducing the size of a model was originally developed for linear systems. When extended to nonlinear systems, some considerations must be faced. First of all, the calculation of the balancing transformation matrix is not unique.
Ivan Dones +2 more
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