On Frequency-Weighted Extended Balanced Truncation
Sribalaji C. Anand, Henrik Sandberg
TL;DR
The paper tackles frequency-weighted extended balanced truncation for both discrete- and continuous-time LTI plants. It introduces a convex proxy for the otherwise nonconvex objective, proves that extended LIs admit block-diagonal solutions, and develops a recursive algorithm with a-priori error bounds, applicable to CT and DT systems. A CT extension is formulated without requiring explicit discretization, leveraging a tunable sampling time to tighten bounds. Numerical examples demonstrate competitive, often superior, error bounds compared with existing methods, validating the approach and highlighting its practical potential despite conservative bounds. Overall, the work provides a principled framework for FW extended truncation with guaranteed error measures and practical CT applicability.
Abstract
This paper addresses the problem of frequency-weighted extended balanced truncation for discrete and continuous-time linear time-invariant plants. We show that the frequency-weighted discrete-time plant admits block-diagonal solutions to both the Lyapunov inequality and its extended form. A recursive algorithm for extended balanced truncation is proposed, together with corresponding a-priori error bounds. Theoretical results are extended to continuous-time systems and validated through numerical examples.