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- W2022105164 abstract "The problem of absolute stability of feedback systems containing a single nonlinearity is considered for the case of the linear transfer function having an equal number of finite poles and zeros. Explicit Liapunov functions are presented and frequency-domain criteria are derived for systems for which the nonlinear function <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>f(cdot)</tex> belongs to the class <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>A_{infty}</tex> ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>f</tex> lies in the first and thirdquadrants) or its subclasses such as monotonically increasing functions <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(finM_{infty})</tex> , odd-monotonic functions <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(fino_{infty})</tex> , and functions witha power-law restriction <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(finP_{infty})</tex> . A new class of functions with restricted asymmetry having the property <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>|f(theta)/f(-0), leqc</tex> for all <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>theta</tex> <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(thetaneq0)</tex> is introduced, and the results obtained can be used to establish stability in some cases even when the Nyquist plot of the linear part transfer function lies in all the four quadrants and the nonlinearity is not necessarily odd. Restrictions on the derivative of the non-linearity have been taken into account by means of a transformation, and the resulting stability criterion is seen to be an improvement over those obtained in some earlier papers." @default.
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- W2022105164 title "Some aspects of the Lur'e problem" @default.
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