Abstract
For feedback systems with a time-varying gain in the feedback path novel conditions are obtained for L 2-stability by proving the positivity of certain operators. The proof is presented for the linear time-varying system and the corresponding results for non-linear time-varying systems can be obtained in a similar fashion. An example illustrates the superiority of the new criterion even though it may not be always superior. An additional requirement to the usual ones is that the time-varying gain must be differentiable twice with respect to time.
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