Frequency- and time-limited balanced truncation for large-scale second-order systems

Development of Frequency Weighted Model Order Reduction Techniques for Discrete-Time One-Dimensional and Two-Dimensional Linear Systems With Error Bounds

“…Recently, a significant amount of research has been conducted on the MOR of large-scale systems, and a number of different MOR approaches have been developed. [7]- [12]. In [7], second-order dynamical systems using structurepreserving balanced truncation approaches are provided, which deals with first-order constrained balanced truncation approaches and apply them to second-order systems utilizing various second-order balanced truncation formulas.…”

“…A substantial amount of study in the MOR of large-scale systems has been done recently, and various methods to MOR have been proposed [7]- [12]. Mathematical modeling aims to analyze dynamical systems, which is an important part of control systems engineering.…”

A comparison of second-order model order reduction methods for an artificial fishtail

“…The codes for the experiments in Section 4.3.2 and the dominant pole approaches in Section 4.3.4 are available as separate packages in [24] and [56] authored by P. Benner and S. W. R. Werner.…”

“…Here, we especially want to compare methods with a global (in time and frequency domains) perspective, such as the several flavors of balanced truncation for second-order systems [14,15,16,17], or (dominant pole based) modal truncation, with more localized methods focusing on the known range of operation frequencies of about 0-10 Hz. The later methods range from simple moment matching (see, e. g., [18,19,20]) approaches with expansion frequencies in this exact range, over twostep, or hybrid methods [21,22] using a moment matching pre-reduction and balancing-based post-processing, to frequency-limited balancing [23,24].…”

Model Reduction for Second‐Order Dynamical Systems Revisited

“…where the time-dependent right-hand sides are Taking the sub-Gramian matrices as in [3,6,9] gives the possibility to get a reduced-order system in secondorder form. Implementations of the different resulting second-order frequency-and time-limited balanced truncation methods can be found in MORLAB [12] for medium-size dense systems and in [13] for large-scale sparse systems using Krylov subspace methods.…”