Optimal Robustness of Port-Hamiltonian Systems

Mehrmann, Volker;Van Dooren, Paul
(2020) SIAM Journal on Matrix Analysis and Applications — Vol. 41, n° 1, p. 134-151 (2020)

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  • Mehrmann, VolkerInstitut fur Mathematik, Berlin, Germany
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  • Van Dooren, PaulUCLouvain
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Abstract
We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given nonpassive one and provide a simple but suboptimal solution.
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Mehrmann, V., & Van Dooren, P. (2020). Optimal Robustness of Port-Hamiltonian Systems. SIAM Journal on Matrix Analysis and Applications, 41(1), 134-151. https://doi.org/10.1137/19m1259092 (Original work published 2020)