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Keywords:
Popov’s inequality; BIBO stability
Popov’s inequality; BIBO stability
Summary:
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.
References:
[1] Doetsch G.: Funktional Transformationen. In: Mathematische Hilfsmittel des Inginieurs, Vol. I (R. Sauer, I. Szabo, eds.), Springer, Berlin 1967, pp. 232–484 MR 0221799
[2] Föllinger O.: Nichtlineare Regelungen. Oldenbourg, München 1993 Zbl 0487.93002
[3] Roïtenberg I. N.: Théorie du contrôle automatique. Publishing House Mir, Moscow 1974 Zbl 0302.93001
[4] Wen J. T.: Time domain and frequency domain conditions for strict positive realness. IEEE Trans. Automat. Control 33 (1988), 988–992 DOI 10.1109/9.7263 | MR 0959031 | Zbl 0664.93013
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