An iterative tangential interpolation framework for model reduction of MIMO systems

We consider model reduction of large-scale MIMO systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which is an iterative algorithm that uses concepts from the Loewner framework. Our algorithm uses low-rank interpolation and iteratively adds interpolation points based on several criteria including minimizing maximum errors. We show there is freedom in the interpolation point selection method, leading to multiple algorithms that have trade-offs between computational complexity and approximation performance. We prove that a weighted \(H_2\) norm of a representative error system is monotonically decreasing as interpolation points are added. Finally, we provide computational results and some comparisons with prior works, demonstrating performance on par with standard model reduction methods.