Arnoldi-based model reduction for fractional order linear systems

In this paper, the Arnoldi-based model reduction methods are employed to fractional order linear time-invariant systems. The resulting model has a smaller dimension, while its fractional order is the same as that of the original system. The error and stability of the reduced model are discussed. And to overcome the local convergence of Padé approximation, the multi-point Arnoldi algorithm, which can recursively generate a reduced-order orthonormal basis from the corresponding Krylov subspace, is used. Numerical examples are given to illustrate the accuracy and efficiency of the proposed methods.