2020/11/13 by Sean Reiter, Reiter, Sean, Damm, Tobias +4
Computer Science · Engineering · Mathematics · #93B10 #93B11 #93C05 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Optimization and Control (math.OC) #Power System Optimization and Stability #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2011.07170
openalex publication_date 2020/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Balanced truncation and singular perturbation approximation for linear dynamical systems yield reduced-order models that satisfy a well-known error bound involving the Hankel singular values. We show that this bound holds with equality for single-input, single-output systems, if the sign parameters corresponding to the truncated Hankel singular values are all equal. These signs are determined by a generalized state-space symmetry property of the corresponding linear model. For a special class of systems having arrowhead realizations, the signs can be determined directly from the off-diagonal entries of the corresponding arrowhead matrix. We describe how such arrowhead systems arise naturally in certain applications of network modeling, and illustrate these results with a power system model that motivated this study.