A Survey of Model Reduction by Balanced Truncation and Some New Results

By Serkan Gugercin, Athanasios C. Antoulas. 2004

905 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f71505e2d4f9bd72e65066406e6436c2a5e8d9c5

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Citations in the corpus

Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment (2014, methodology): “, POD [8], balanced truncation [16, 5], proper generalized decomposition [42], among othe rs).”
Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, methodology): “For example, available surrogate models may include projection-based reduced models [44, 43, 24, 3], data-fit interpolation and regression models [21], machine-learning-based support vector machines (SVMs) [16, 48, 11], and simplified-physics models [2, 37].”
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition (2008, positive): “However, the MPE approach is applicable to other projection-based model reduction techniques, such as balanced truncation [15], [22], [31], [37] and”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “For stable linear time-invariant systems, balanced truncation provides a basis that guarantees asymptotically stable reduced systems and provides an error bound [7, 88].”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, neutral): “See [34, 115, 183] for overviews of possible choices and corresponding properties preserved in the reduced models.”
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples (2012, methodology): “Modal analysis (linear or non-linear normal modes), but also the moment matching method [2,7] and balanced truncation [11, 26] belong to this first family.”
Proper orthogonal decomposition for optimality systems (2008, neutral): “Received March 24, 2006.”
Application of Balanced Realizations for Model-Order Reduction of Dynamic Power System Equivalents (2016, background): “In recent years, however, significant progress has been achieved in solving large Lyapunov equations [39], [40].”
Power System Stability With a High Penetration of Inverter-Based Resources (2023, methodology): “There are other model truncation methods available in the systems theory, but they are not widely used in power engineering [54], [55].”
Hessian‐based model reduction for large‐scale systems with initial‐condition inputs (2008, methodology): “Methods to compute the basis in the largescale setting include Krylov-subspace methods [15, 16, 19], approximate balanced truncation [20,27,28,31], and proper orthogonal decomposition (POD) [13,24,30].”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “For a survey on balanced truncation model reduction see [107].”
Reduced-Order Models for Representing Converters in Power System Studies (2018, background): “moment matching, modal truncation, and so on [22], [23].”
A Survey on Model Reduction of Coupled Systems (2008, methodology): “Apart from the balanced truncation method considered here, other balancingbased model reduction techniques have been developed, see [32, 47].”