Guaranteed passive balancing transformations for model order reduction

Abstract—The major concerns in state-of-the-art model reduc-tion algorithms are: achieving accuratemodels of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms, such as PRIMA, generate guaranteed-passive models for systems with special internal structure, using numerically stable and effi-cient Krylov-subspace iterations. Truncated balanced realization (TBR) algorithms, as used to date in the design automation com-munity, can achieve smaller models with better error control, but do not necessarily preserve passivity. In this paper, we show how to construct TBR-like methods that generate guaranteed passive re-duced models and in addition are applicable to state-space systems with arbitrary internal structure. Index Terms—Passive reduced-order modeling, truncated bal-anced realization (TBR), Lur’e equations, Lyapunov equations, Krylov subspace