  We consider the autonomous dynamical system $x' = Ax$, with $A \in
\mathbb{R}^{n\times n}$. This linear dynamical system is said to be
asymptotically stable if all of the eigenvalues of A lie in the open left-half
of the complex plane. In this case, the matrix A is said to be Hurwitz stable
or shortly a stable matrix. In practice, stability of a system can be violated
because of arbitrarily small perturbations such as modeling errors. In such
cases, one deals with the robust stability of the system rather than its
stability. The system above is said to be robustly stable if the system, as
well as all of its arbitrarily small perturbations, are stable. To measure the
robustness of the system subject to perturbations, a quantity of interest is
the stability radius or in other words distance to instability. In this paper
we focus on the estimation of the structured real stability radius for
large-scale systems. We propose a subspace framework to estimate the structured
real stability radius and prove that our new method converges at a quadratic
rate in theory. Our method benefits from a one-sided interpolatory model order
reduction technique, in a sense that the left and the right subspaces are the
same. The quadratic convergence of the method is due to the certain Hermite
interpolation properties between the full and reduced problems. The proposed
framework estimate the structured real stability radius for large-scale systems
efficiently. The efficiency of the method is demonstrated on several numerical
experiments. Key words. real stability radius, structured, large-scale,
projection, singular values, Hermite interpolation, model order reduction,
greedy search.
