An approach to the reduction of multivariable systems with various numbers of inputs and outputs

The analysis and synthesis of high-order systems are computationally difficult and cumbersome. Accordingly, there is a need for obtaining reduced models for the high-order system so that an analogue or digital simulation of the system is possible. An algebraic method is proposed in the frequency domain to obtain the reduced models of singlevariable systems as well as multivariable systems. The method of matrix-continued fraction and the mixed method, which utilizes both the dominant-eigenvalue concept and matrix-continued fraction approach, are extended to obtain the reduced models. The reduced model is always stable and it retains the dominant performance of the original system. A complete computer-oriented algorithm is established for the simplification.