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$L_2$-Stability of Nonstationary Feedback Systems: Frequency-Domain Criteria

Sundareshan, Malur K and Thathachar, MAL (1974) $L_2$-Stability of Nonstationary Feedback Systems: Frequency-Domain Criteria. In: IEEE Transactions on Automatic Control, 19 (3). pp. 217-224.


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A frequency-domain positivity condition is derived for linear time-varying operators in $L_2$ and is used to develop $L_2$ stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in $L_2$ with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Item Type: Journal Article
Publication: IEEE Transactions on Automatic Control
Publisher: IEEE
Additional Information: © 1974 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 23 Nov 2007
Last Modified: 19 Sep 2010 04:20
URI: http://eprints.iisc.ac.in/id/eprint/3720

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