AAA rational approximation for time domain model order reduction

In this paper an extension of the Adaptive Antoulas-Anderson (AAA) Model Order Reduction (MOR) method to time-domain data is defined, referred to as Time-Domain AAA (TDAAA). Inspired by other rational approximation time-domain MOR methods, like Time-Domain Vector Fitting (TDVF) and Time-Domain Loewner Framework (TDLF), TDAAA combines the adaptivity and flexibility of the AAA method in the frequency domain with an error minimization in the time domain. This combination makes the method an interesting alternative to fully time-domain or frequency-domain MOR methods. A combination of AAA and TDVF is also proposed, called AAA-TDVF, where the initial TDVF poles are selected by AAA. This new poles initialization improves both accuracy and convergence speed. Both TDAAA and TDVF are discussed in detail and their performance is compared on a benchmark LTI system.