Model order reduction in parallel of discrete-time linear systems based on Meixner and Krawtchouk polynomials

In this paper, based on the partition technique, we use Meixner and Krawtchouk polynomials to present an input-independent model order reduction method. Our main contributions are twofold. First, the explicit difference relations of Meixner polynomials and Krawtchouk polynomials are expressed in an unified form. The parallel computation is carried out on the partitioned subsystems using the Krylov subspaces by which one can generate reduced systems independent of the expansion coefficients of input and can save the computation time. Second, a parallel adaptive enrichment strategy is used to choose the reduced order of reduced systems. Theoretical analysis shows that the proposed method characterizes the property of invariable coefficients. Finally, two numerical examples demonstrate that the proposed method achieves good reduction results in terms of accuracy and reduced CPU time.