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- W2034223616 abstract "The purpose of this letter is to initiate a study of the question of L <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>p</inf> (p≥1) stability of a larger class of nonlinear feedback systems whose forward loop is represented by a truncated Volterra series of the form (Ax)(t) = Σ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n = 1</inf> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m < ∞</sup> ∫ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</sup> ∫ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</sup> K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</inf> (t; τ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</inf> , ... τ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</inf> ) Π <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i = 1</inf> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> x(τ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</inf> )dτ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</inf> . It is demonstrated that under suitable conditions the open-loop system A is continuous and boundaed, and maps L <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>p</inf> [0, ∞) into L <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>p</inf> [0, ∞). It is shown that if the corresponding (unity gain) feedback system has a solution in some Lebesgue class L <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>p</inf> (0 > p ≥ ∞), then the output of the feedback system belongs to the same class as the input." @default.
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- W2034223616 date "1969-01-01" @default.
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- W2034223616 title "On the Lp(p≥1) stability of a class of nonlinear systems" @default.
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- W2034223616 doi "https://doi.org/10.1109/proc.1969.7418" @default.
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