  In this paper, we consider the problem of approximating a given matrix with a
matrix whose eigenvalues lie in some specific region \Omega, within the complex
plane. More precisely, we consider three types of regions and their
intersections: conic sectors, vertical strips and disks. We refer to this
problem as the nearest \Omega-stable matrix problem. This includes as special
cases the stable matrices for continuous and discrete time linear
time-invariant systems. In order to achieve this goal, we parametrize this
problem using dissipative Hamiltonian matrices and linear matrix inequalities.
This leads to a reformulation of the problem with a convex feasible set. By
applying a block coordinate descent method on this reformulation, we are able
to compute solutions to the approximation problem, which is illustrated on some
examples.
