Geodesic
Time-domain and parametric $L^2$-properties corresponding to Popov inequality
Kybernetika, Tome 38 (2002) no. 5, p. [617].

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For Popov’s frequency-domain inequality a general solution is constructed in $L^2$, which relies on the strict positive realness of a generating function. This solution allows revealing time-domain properties, equivalent to the fulfilment of Popov’s inequality in the frequency-domain. Particular aspects occurring in the dynamics of the linear subsystem involved in Popov’s inequality are further explored for step response, as representing a usual characterization in control system analysis. It is also shown that such behavioural particularities are directly related to the BIBO stability of the linear subsystem.
Classification : 93D10, 93D25
Keywords: Popov’s inequality; BIBO stability 
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     author = {Voicu, Mihail and Pastravanu, Octavian},
     title = {Time-domain and parametric $L^2$-properties corresponding to {Popov} inequality},
     journal = {Kybernetika},
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     publisher = {mathdoc},
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     number = {5},
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     zbl = {1265.93219},
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     url = {http://geodesic.mathdoc.fr/item/KYB_2002__38_5_a9/}
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Voicu, Mihail; Pastravanu, Octavian. Time-domain and parametric $L^2$-properties corresponding to Popov inequality. Kybernetika, Tome 38 (2002) no. 5, p. [617]. http://geodesic.mathdoc.fr/item/KYB_2002__38_5_a9/