MIMO Model Order Reduction by Padé-Markov Least Squares and Frequency Data Fitting

This paper presents a new analytical method for model order reduction of dynamic systems, appli- cable to both SISO and MIMO models. The method is structured into two stages: the first stage computes a common characteristic polynomial using Pad´e coeffcients and Markov parameters; the second stage estimates the gain and zeros by optimally fitting the frequency response data using a quadratic norm criterion. The resulting reduced-order model is obtained by solving systems of linear equations, avoiding iterative procedures and numerical optimization algorithms. The method extends existing approaches by ensuring a unified denominator across all MIMO channels and provides an exact analytical solution for the optimal numerator coeffcients. The convexity of the cost function guaran- tees global optimality. The effectiveness and versatility of the proposed approach are demonstrated through three case studies, including systems with unstable and non-minimum phase characteristics. The results show that the method yields competitive accuracy compared to the available techniques in the frequency domain.