## 7 Conclusions and Future Work  
In this paper, we presented a stability-preserving model reduction and interpolation method for optimizing the vibration characteristics of beam-like structures. The proposed approach integrates parametric model order reduction with an interpolation framework, which ensures stability and provides an upper bound on the deviation of interpolated models in the \(H_{\text{inf}}\) norm. The method was extended to multiple-input multiple-output systems. Using geometric interpolation techniques within the hyperbolic plane, we constructed all possible interpolation trajectories that preserve the stability characteristics of the original system within this framework. Additionally, we introduced a criterion for assessing the adequacy of parameter sampling in the interpolation process, ensuring accurate pole matching.  
The numerical example demonstrated the feasibility of deriving a reduced-order Bernoulli beam model from finite element method (FEM) data. The model's accuracy was validated against theoretical calculations.  
Several directions will be pursued to enhance the accuracy, robustness, and applicability of the proposed reduced-order modeling framework. A key focus will be on refining the interpolation strategy for residuals. In particular, the rationale behind the current use of linear interpolation will be critically examined, and alternative interpolation functions will be explored to more effectively capture the underlying system dynamics.  
Further developments will also consider the extension of the methodology to accommodate vector-valued parameters, thus enabling the modeling of more complex structural variations. Additionally, incorporating higher-order sensitivity terms into the pole-matching process represents another promising direction to increase model fidelity.  
Attention will also be directed toward the selection of the projection line, with a specific emphasis on its alignment with the neutral axis. Optimizing this aspect could yield improvements in the consistency and accuracy of the reduced models.  
Another important area for future research involves the reduction of conservatism in the estimation of the maximum singular value for MIMO systems. While the Gerschgorin theorem provides a computationally efficient bound, it can result in overly conservative estimates. To address this, more precise techniques and specific estimation methods will be explored.  
Moreover, the framework will be extended to rigorously analyze the propagation of approximation errors stemming from the polynomial fitting of deflection data.  
Finally, the integration of previously established models, such as the Timoshenko beam model from [20; 21], will be further explored. Given that this model adheres to the same second-order formulation as Equation (10), it can be seamlessly incorporated into the current framework. However, refinement of the reduction process remains necessary to fully leverage its potential.  
Conceptualization, I.G.; methodology, I.G.; formal analysis, I.G.; data curation, I.G.; writing--original draft preparation, I.G.; writing--review and editing, I.G.; visualization, I.G.; supervision, R.S.; project administration, R.S.; funding acquisition, R.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors acknowledge the financial support of Obuda University.  
Author [PERSON] was employed by the company Inceptive Mechatronics Kft. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.