5 papers
Data-driven Implementations of Various Generalizations of Balanced Truncation
Umair Zulfiqar, Qiu-Yan Song, Zhi-Hua Xiao +1
Quadrature-based approximation of Gramians in standard balanced truncation yields a non-intrusive, data-driven implementation that requires only transfer function samples on the im…
A Unified Low-rank ADI Framework with Shared Linear Solves for Simultaneously Solving Multiple Lyapunov, Sylvester, and Riccati Equations
Umair Zulfiqar, Zhong-Yi Huang, Qiu-Yan Song +1
The alternating direction implicit (ADI) methods are computationally efficient and numerically effective tools for computing low-rank solutions of large-scale linear matrix equatio…
-optimal Model Reduction of Linear Quadratic Output Systems in Finite Frequency Range
Umair Zulfiqar, Zhi-Hua Xiao, Qiu-Yan Song +2
In frequency-limited model order reduction, the objective is to maintain the frequency response of the original system within a specified frequency range in the reduced-order model…
Balanced Truncation via Tangential Interpolation
Umair Zulfiqar, Zhi-Hua Xiao, Qiu-yan Song +1
This paper examines the construction of rth-order truncated balanced realizations via tangential interpolation at r specified interpolation points. It is demonstrated that when the…
Time-limited H2-optimal Model Order Reduction of Linear Systems with Quadratic Outputs
Umair Zulfiqar, Zhi-Hua Xiao, Qiu-Yan Song +2
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear t…