  In this paper, we introduce the following concept which generalizes known
definitions of multiplicative and additive $D$-stability, Schur $D$-stability,
$H$-stability, $D$-hyperbolicity and many others. Given a subset ${\mathfrak D}
\subset {\mathbb C}$, a matrix class ${\mathcal G} \subset {\mathcal M}^{n
\times n}$ and a binary operation $\circ$ on ${\mathcal M}^{n \times n}$, an $n
\times n$ matrix $\mathbf A$ is called $({\mathfrak D}, {\mathcal G},
\circ)$-stable if $\sigma({\mathbf G}\circ {\mathbf A}) \subset {\mathfrak D}$
for any ${\mathbf G} \in {\mathcal G}$. Such an approach allows us to unite
several well-known matrix problems and to consider common ways of their
analysis. Here, we make a survey of existing results and open problems on
different types of stability, study basic properties of $({\mathfrak D},
{\mathcal G}, \circ)$-stable matrices and relations between different
$({\mathfrak D}, {\mathcal G}, \circ)$-stability classes.
