Abstract
Abstract This paper presents new criteria for the L 2-input, L 2-output stability of a class of feedback systems containing a time-invariant convolution operator and a time varying non-linearity in cascade, in a negative feedback loop. These are sufficient conditions for the system stability derived using the multiplier concept and involve certain time-domain conditions on the multiplier. The method of derivation draws on the theory of positivity of compositions of operators and time-varying gains and necessitates an upper bound on the rate of variation of the time-varying gain.
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