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In this paper, we characterize the set of static-state feedbacks thatstabilize a given continuous linear-time invariant system pair usingdissipative Hamiltonian matrices. This characterization results in aparametrization of feedbacks in terms of skew-symmetric and symmetric positivesemidefinite matrices, and leads to a semidefinite program that computes astatic-state stabilizing feedback. This characterization also allows us topropose an algorithm that computes minimal-norm static feedbacks. Thetheoretical results extend to the static-output feedback (SOF) problem, and wealso propose an algorithm to tackle this problem. We illustrate theeffectiveness of our algorithm compared to state-of-the-art methods for the SOFproblem on numerous numerical examples from the COMPLeIB library.

Minimal-norm static feedbacks using dissipative Hamiltonian matrices