4 CONCLUSIONS
This paper is demonstrating a point of view that
seemed very natural when absolute stability i.e. ro-
bust global asymptotic stability for systems with sec-
tor restricted nonlinear functions was investigated.
This point of view is that robust stability of linear
systems should imply the same property for non-
linear systems also, at least for those with sector
restricted nonlinearities. Such a point of view is
transparent throughout all research concerning the
so called Aizerman and Kalman problems (Popov,
1973),(R˘asvan, 1975) and geometric similarities of
the Nyquist and Popov frequency domain criteria
strengthened it. Stating it, obviously is not enough;
this position paper is pointing to critical analysis and
further research, mainly application oriented. We
have chosen the ﬁeld of aircraft oscillations to illus-
trate this point of view for its practical importance
(proved by the intense research activities around PIO
problem) as well as for its feedback-based modeling
of the dynamics: control appears here as a genuine
hidden technology and hidden paradigm.
Since the ﬁeld of aircraft dynamics and handling
qualities has very strict requirements and procedures,
the amount of the necessary research appears to be
high and with a certain degree of complexity. The
point of view stated here is to be applied possibly to
all cases of PIO I i.e. corresponding to fully linearized
systems; for the entire set of criteria, see (Anon.,
2000),(Klyde et al., 1995). But for each criterion one
may wish to consider several cases of pilot models.
For all these cases we have to consider the PIO II i.e.
the nonlinear, rate limited counterpart. But, besides
the comparison of the PIO I criteria and of their non-
linear counterpart, a comparison with the other PIO II
criteria, obtained independently of the approach pre-
sented in this paper is also necessary.
All this analysis and various comparison of the
criteria contain the necessary amount of critical
assessment of the present position paper proposal.
To this we add the speciﬁc PIO approach in aircraft
studies: conversion in a checkable form and applica-
tion on “real data” stored in the aviation databases.
Nevertheless it is hoped to follow the approach de-
scribed here in the next research on other PIO criteria.
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