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$L_2$-Stability of Linear Time-Varying Systems--Conditions Involving Noncausal Multipliers

Sundareshan, Malur K and Thathachar, MAL (1972) $L_2$-Stability of Linear Time-Varying Systems--Conditions Involving Noncausal Multipliers. In: IEEE Transactions on Automatic Control, 17 (4). pp. 504-510.


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New criteria in the multiplier form are presented for the input-output stability in the $L_2$-space of a linear system with a time-varying element k(t)in a feedback loop. These are sufficient conditions for the system stability and involve conditions on the shifted imaginary-axis behavior of the multipliers. The criteria permit the use of noncausal multipliers, and it is shown that this necessitates dk/dt to be bounded from above as well as from below. The method of derivation draws on the theory of positivity of compositions of operators and time-varying gains, and the results are shown to be more general than the existing criteria.

Item Type: Journal Article
Publication: IEEE Transactions on Automatic Control
Publisher: IEEE
Additional Information: �©1972 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: 13 Sep 2005
Last Modified: 19 Sep 2010 04:20
URI: http://eprints.iisc.ac.in/id/eprint/3635

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