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On the optimality of the proper orthogonal decomposition and balanced truncation
2008 47th IEEE Conference on Decision and Control, 2008The proper orthogonal decomposition (POD), also known as Karhunen-Loeve decomposition or principal component analysis, and balanced truncation, are shown to be optimal in the sense of distance minimizations in spaces of Hilbert-Schmidt or trace-class 2 integral operators. Both POD and balanced truncation are shown to be optimal approximations by finite
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Positivity Preserving Balanced Truncation for Descriptor Systems
SIAM Journal on Control and Optimization, 2009We propose a model reduction method for positive systems that ensures the positivity of the reduced-order model. In the standard as well as in the descriptor case, for continuous-time and discrete-time systems, our approach is based on constructing diagonal solutions of Lyapunov inequalities. These are linear matrix inequalities (LMIs), which are shown
Timo Reis, Elena Virnik
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A tangential method for the balanced truncation in model reduction
Numerical Algorithms, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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 ...
Bart Besselink +3 more
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Diagonal balanced truncation of discrete delay systems
Automatica, 1999The author introduces a new model reduction method for discrete delay systems, different from the traditional method, where the reduced system is also a discrete delay system of a smaller size in the dimension of the state. The author considers the following discrete state delay system \[ G:\begin{aligned} & x(k+1)=A_0x(k)+A_1x(k-N)+Bu(k)\\ & y(k)=Cx(k)
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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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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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Balanced Truncation Model Reduction for Symmetric Second Order Systems---A Passivity-Based Approach
SIAM Journal on Matrix Analysis and Applications, 2021Matthias Voigt, Timo Reis
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Balanced truncation model reduction of second-order systems
Mathematical and Computer Modelling of Dynamical Systems, 2008Tatjana Stykel, Timo Reis
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