On Frequency-Weighted Extended Balanced Truncation

TL;DR

This paper develops a frequency-weighted extended balanced truncation method for LTI systems, providing theoretical guarantees and recursive algorithms, validated through numerical examples for both discrete and continuous-time systems.

Contribution

It introduces a recursive algorithm for frequency-weighted extended balanced truncation with proven error bounds, extending the approach to continuous-time systems.

Findings

Block-diagonal solutions to Lyapunov inequalities are shown for frequency-weighted discrete-time plants.

A recursive algorithm for extended balanced truncation is proposed.

Numerical examples validate the theoretical results for both discrete and continuous-time systems.

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.