  In this paper, we characterize the set of static-state feedbacks that
stabilize a given continuous linear-time invariant system pair using
dissipative Hamiltonian matrices. This characterization results in a
parametrization of feedbacks in terms of skew-symmetric and symmetric positive
semidefinite matrices, and leads to a semidefinite program that computes a
static-state stabilizing feedback. This characterization also allows us to
propose an algorithm that computes minimal-norm static feedbacks. The
theoretical results extend to the static-output feedback (SOF) problem, and we
also propose an algorithm to tackle this problem. We illustrate the
effectiveness of our algorithm compared to state-of-the-art methods for the SOF
problem on numerous numerical examples from the COMPLeIB library.
