Identification of Low Order Systems in a Loewner Framework.

Area of Science:

• Systems engineering
• Control theory
• Numerical analysis

Background:

• Accurate system identification is crucial for control and analysis.
• Traditional methods like Hankel matrix-based identification can be computationally intensive and yield high-order models.
• Non-parametric identification from time-domain data presents unique challenges.

Purpose of the Study:

• To develop a novel non-parametric method for identifying low-order system models from time-domain data.
• To compare the efficiency of Loewner-based interpolation and reduction with traditional Hankel matrix methods.
• To demonstrate the effectiveness of the proposed approach through numerical examples.

Main Methods:

• Utilizing Caratheodory Fejer and Loewner-based interpolation for system realization.
• Applying a Loewner matrix Balanced Reduction (LBR) step for model order reduction.
• Employing Zolotarev numbers to analyze singular value decay rates.

Main Results:

• The Loewner matrix serves as an effective estimator for the trace norm of a system.
• Singular values in the Loewner matrix exhibit significantly faster decay rates than those in the Hankel matrix.
• Loewner-based methods achieve lower-order system models with comparable error bounds.

Conclusions:

• The proposed Loewner-based method provides a more efficient approach to non-parametric system identification.
• This technique yields reduced-order models with improved accuracy and computational efficiency.
• The findings offer a valuable alternative for system identification in various engineering applications.