Dimension reduction based on approximate gramians via Laguerre polynomials for coupled systems

Abstract

In this paper, we focus on the topic of model order reduction (MOR) for coupled systems. At first, an approximation via Laguerre polynomials expansions to controllability and observability gramians for such systems are presented, which provides a low-rank decomposition form whose factors are constructed from a recurrence formula instead of Lyapunov equations. Then, in combination of balanced truncation and dominant subspace projection method, a series of MOR algorithms are proposed that preserve the coupled structures. What’s more, some main properties of reduced-order models, such as stability preservation, are well discussed. Finally, three numerical simulations are provided to illustrate the effectiveness of our algorithms.