Iterative Stability Enforcement in Adaptive Antoulas-Anderson Algorithms for H_2 Model Reduction

This paper presents an extension of the Adaptive Antoulas-Anderson (AAA) algorithm for rational modeling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm builds rational approximations of multi-input signals with a common set of stable poles. A new methodology is presented for iteratively enforcing the stability constraint on the poles. We demonstrate the strengths of this approach compared to the stability enforcement in the FastAAA algorithm. Results using the smiAAA algorithm are compared with the commonly used Vector Fitting algorithm and the more recently published Rational Krylov fitting (RKFIT) algorithm. The Vector Fitting and RKFIT algorithms both require the user to input the number of poles to use in the approximations. If the final approximation is not accurate enough, the user must restart the Vector Fitting or RKFIT algorithm with a larger number of poles and/or a new starting location for the poles. In contrast, the smiAAA algorithm is designed to allow the user to simply input the desired accuracy of the approximations, and the necessary number of poles is detected automatically. This permits users to produce approximations of a desired accuracy with no knowledge about the underlying order of the system being approximated, preventing the algorithm from ever needing to be rerun. An additional feature for preventing extraneous poles from being returned by the AAA algorithm is also discussed. The cause of these extraneous poles is efficiently detected and removed by our presented methodology. The examples presented demonstrate that the smiAAA algorithm can efficiently produce approximations of similar or better accuracy than the Vector Fitting and RKFIT algorithms while requiring less input from the user.