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- W3143981090 abstract "In this paper, we find necessary and sufficient conditions to identify pairs of matrices $X$ and $Y$ for which there exists $Delta in mathbb C^{n,n}$ such that $Delta+Delta^*$ is positive semidefinite and $Delta X=Y$. Such a $Delta$ is called a dissipative mapping taking $X$ to $Y$. We also provide two different characterizations for the set of all dissipative mappings, and use them to characterize the unique dissipative mapping with minimal Frobenius norm. The minimal-norm dissipative mapping is then used to determine the distance to asymptotic instability for dissipative-Hamiltonian systems under general structure-preserving perturbations. We illustrate our results over some numerical examples and compare them with those of Mehl, Mehrmann and Sharma (Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations, SIAM J. Mat. Anal. Appl. 37 (4): 1625-1654, 2016)." @default.
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- W3143981090 date "2021-04-02" @default.
- W3143981090 modified "2023-09-27" @default.
- W3143981090 title "Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems" @default.
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