Pade type model order reduction for multivariable systems using routh approximation

A method of obtaining reduced order models for multivariable systems is described. It is shown that the method has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. Irrespective of whether the original multivariable system is described in state space form or in the transfer matrix form, the proposed method yields the reduced order models in state space form. In this method the Routh approximation is used to formulate the common denominator polynomial of a reduced order model. This is used to describe the structure of A_r matrix. The matrices B_r and C_r are chosen appropriately and some of the elements of B_r/C_r matrices are specified in such a way that after matching time moments/Markov parameters, the resulting equations are linear in the unknown elements of B_r and C_r matrices. The procedure is illustrated via a numerical example.