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<p>This paper presents a new analytical method for model order reduction of dynamic systems, applicable to both SISO and MIMO models. The method is structured into two stages: the first stage computes a common characteristic polynomial using Padé coefficients 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 coefficients. The convexity of the cost function guarantees 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 indicate that the method achieves competitive accuracy compared to existing techniques in the frequency domain.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Marcelo A. Oliveira,
  • Roberto Ades,
  • Paulo César Pellanda

摘要

This paper presents a new analytical method for model order reduction of dynamic systems, applicable to both SISO and MIMO models. The method is structured into two stages: the first stage computes a common characteristic polynomial using Padé coefficients 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 coefficients. The convexity of the cost function guarantees 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 indicate that the method achieves competitive accuracy compared to existing techniques in the frequency domain.