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On Optimal Solutions to Two-Block H∞ Problems

Hassibi, Babak and Kailath, Thomas (1998) On Optimal Solutions to Two-Block H∞ Problems. In: Proceedings of the 1998 American Control Conference. Vol.3. IEEE , Piscataway, NJ, pp. 1975-1979. ISBN 0-7803-4530-4.

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In this paper we obtain a new formula for the minimum achievable disturbance attenuation in two-block H∞ problems. This new formula has the same structure as the optimal H∞ norm formula for noncausal problems, except that doubly- infinite (so-called Laurent) operators must be replaced by semi-infinite (so-called Toeplitz) operators. The benefit of the new formula is that it allows us to find explicit expressions for the optimal H∞ norm in several important cases: the equalization problem (or its dual, the tracking problem), and the problem of filtering signals in additive noise. Furthermore, it leads us to the concepts of “worst-case non-estimability”, corresponding to when causal filters cannot reduce the H∞ norms from their a priori values, and “worst-case complete estimability”, corresponding to when causal filters offer the same H∞ performance as noncausal ones. We also obtain an explicit characterization of worst-case non-estimability and study the consequences to the problem of equalization with finite delay.

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Additional Information:© 1998 IEEE. This work was supported in part by DARPA through the Department of Air Force under contract F49620-95-1-0525-P00001 and by the Joint Service Electronics Program at Stanford under contract DAAH04-94-G-0058-P00003.
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Air Force Office of Scientific Research (AFOSR)F49620-95-1-0525-P00001
Joint Service Electronics ProgramDAAH04-94-G-0058-P00003
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54909
Deposited By: Shirley Slattery
Deposited On:19 Feb 2015 00:18
Last Modified:10 Nov 2021 20:39

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