A modified Krylov subspace model reduction method based on the Chebyshev polynomials

In this paper, we present a modified Krylov subspace model reduction method for linear time invariable systems based on the Chebyshev polynomials. Noting the structure of the Chebyshev polynomial coefficient matrices, which are calculated approximately via the Chebyshev polynomial expansion of the state variable, we employ Krylov subspace to construct decent projection matrices. A reduced order system is produced in two-sided projection framework by combining the time and the frequency domain analysis. Two numerical examples are used to illustrate the efficiency of the method.