Balanced truncation model reduction for symmetric second order systems -- A passivity-based approach

TL;DR

This paper presents a passivity-based balanced truncation method for symmetric second order systems that ensures stability, passivity, and structure preservation, with an a priori error bound.

Contribution

It introduces a novel model reduction technique that guarantees stability, passivity, and structure preservation for symmetric second order systems using positive real balanced truncation.

Findings

Guarantees asymptotic stability and passivity of reduced models

Ensures positive definiteness of mass and stiffness matrices

Provides an a priori gap metric error bound

Abstract

We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees asymptotic stability and passivity of the reduced order model as well as the positive definiteness of the mass and stiffness matrices. Moreover, we receive an a priori gap metric error bound. Finally, we show that our method based on positive real balanced truncation preserves the structure of overdamped second order systems.