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- W2076557130 abstract "Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) ⩾ δ > 0 ∀ω ϵ (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 ⩽ β ⩽ 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt ⩽ 1 − ϵ, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ϵ > 0, and ∝0∞¦y3(t)¦ dt < 12c2, c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria." @default.
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- W2076557130 date "1973-06-01" @default.
- W2076557130 modified "2023-09-26" @default.
- W2076557130 title "On the L2-stability of a class of nonlinear systems" @default.
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- W2076557130 doi "https://doi.org/10.1016/0022-247x(73)90171-6" @default.
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