Characterization of the dissipative mappings and their application to perturbations of dissipative‐Hamiltonian systems

Abstract In this article, we find necessary and sufficient conditions to identify pairs of matrices X Y for which there exists such that is positive semidefinite . Such a called dissipative mapping taking We also provide two different characterizations the set all mappings, use them characterize unique with minimal Frobenius norm. The minimal‐norm then used determine distance asymptotic instability dissipative‐Hamiltonian systems under general structure‐preserving perturbations. illustrate our results over some numerical examples compare those Mehl, Mehrmann, Sharma (Stability radii linear Hamiltonian dissipation perturbations, SIAM J Matrix Anal Appl , 37(4):1625–54, 2016).