Model Reduction Based on Matrix Polynomials

Abstract

Model reduction is an active field of research. It is the approximation of dynamical systems into systems having the same behavior and properties but with smaller order. Model reduction techniques presented in the past [1]–[4] have tried to improve: storage, computational speed and accuracy. Most of the methods can be categorized into two main approaches: Krylov based subspaces and Truncation. Some of the methods proposed include: the Padé via lanczos method, the Arnoldi and Prima method, the Laguene method, the balanced truncation method, the optimal Hankel norm method and the Proper orthogonal decomposition (POD) method. In this contribution, we present a method for multi input multi output linear systems. This method is based on matrix polynomials and block poles. Other algorithms are based on the factorization of transfer functions by eliminating block poles. The main contribution of this method is the capability of eliminating multiple block poles at the same time. This method is particularly suitable if the given system is in matrix transfer function form. The presented method is implemented in MATLAB in order to provide a systematic method for the model order reduction of MIMO linear systems. In order to illustrate the use of this method in robotics, a simple application is presented.