In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established
itself as the method of choice for solving rational approximation problems.
Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant
(LTI) systems represents one of the many applications in which this algorithm
has proven to be successful since it typically generates reduced-order models
(ROMs) efficiently and in an automated way. Despite its effectiveness and
numerical reliability, the classical AAA algorithm is not guaranteed to return
a ROM that retains the same structural features of the underlying dynamical
system, such as the stability of the dynamics. In this paper, we propose a
novel algebraic characterization for the stability of ROMs with transfer
function obeying the AAA barycentric structure. We use this characterization to
formulate a set of convex constraints on the free coefficients of the AAA model
that, whenever verified, guarantee by construction the asymptotic stability of
the resulting ROM. We suggest how to embed such constraints within the AAA
optimization routine, and we validate experimentally the effectiveness of the
resulting algorithm, named stabAAA, over a set of relevant MOR applications.Comment: 29 pages, 4 figures. With respect to the previous version: typos have
been corrected and an appendix has been adde