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Vol: 56(70) No: 1 / March 2011 Theoretical Background for PIO II Analysis Vladimir Răsvan Department of Automatic Control, University of Craiova, A.I. Cuza str., no. 13, 200585, Craiova, Romania, phone: (+40) 251-438198, e-mail: vrasvan@automation.ucv.ro, web: www.automation.ucv.ro/Romana/membri/Rasvan%20Vladimir/VRasvan.htm Daniela Danciu Department of Automatic Control, University of Craiova, A.I. Cuza str., no. 13, 200585, Craiova, Romania, phone: (+40) 251-438198, e-mail: daniela@automation.ucv.ro, web: www.automation.ucv.ro/Romana/membri/Daniela%20Danciu/DDanciu.htm Keywords: P(ilot) I(n-the-Loop) O(scillations), robustness, absolute stability, Popov frequency domain inequalities Abstract P(ilot) I(n-the-Loop) O(scillations) represent a technical phenomenon whose interpretation reveals in a very striking way the idea of feedback control as hidden technology. In fact these are self-sustained oscillations occurring in a feedback loop containing the airframe dynamics and the pilot dynamics viewed as a controller. The second category PIO II is triggered by the position and rate limiters – functional blocks containing a saturation function. Since saturation is a sector restricted and monotone nonlinearity, the PIO II may be approached within the theory of absolute stability. Consequently, some three basic PIO II approaches (robust control, Popov approach and the IQC approach) appear as belonging to the same methodological family. The paper presents these facts under a common point of view – that of the frequency domain stability inequalities. The specific application has the sector conditions fulfilled only on a finite state space domain: the estimate of this domain is obtained using a Liapunov function of the type “quadratic form plus integral” whose existence follows from the frequency domain inequality. References [1] V. Răsvan and D. 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