Balanced truncation model order reduction in limited time intervals for large systems

摘要

In this article we investigate model order reduction of large-scale systemsusing time-limited balanced truncation, which restricts the well known balancedtruncation framework to prescribed finite time intervals. The main emphasis ison the efficient numerical realization of this model reduction approach in caseof large system dimensions. We discuss numerical methods to deal with theresulting matrix exponential functions and Lyapunov equations which are solvedfor low-rank approximations. Our main tool for this purpose are rational Krylovsubspace methods. We also discuss the eigenvalue decay and numerical rank ofthe solutions of the Lyapunov equations. These results, and also numericalexperiments, will show that depending on the final time horizon, the numericalrank of the Lyapunov solutions in time-limited balanced truncation can besmaller compared to standard balanced truncation. In numerical experiments wetest the approaches for computing low-rank factors of the involved Lyapunovsolutions and illustrate that time-limited balanced truncation can generatereduced order models having a higher accuracy in the considered time region.