Model order reduction for discrete-time linear systems with the discrete-time polynomials

Abstract

In this article, the two-sided model order reduction (MOR) method based on the Charlier and discrete Laguerre polynomials is proposed for large-scale discrete-time linear systems. We first introduce some definitions and results of Charlier polynomials, which are extended from continuous orthogonal polynomial. Then we design the algorithm. The main assumption is that the solution is in the space spanned by Charlier orthogonal polynomials, and then the expansion coefficients of the solution are calculated to generate the projection matrix. Further, combining the frequency-domain techniques with the discrete-time domain techniques, we develop the two-sided projection MOR method, which is a hybrid reduction technique that can possess the nice properties of these two methods. The proposed approach has good computational efficiency and preserves the internal stability under certain condition. Numerical experiments verify the feasibility and effectiveness of the proposed method.