GuaranteedH∞robustness bounds for Wiener filtering and prediction

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Abstract
The paper deals with special classes ofH∞estimation problems, where the signal to be estimated coincides with the uncorrupted measured output. Explicit bounds on the difference between nominal and actualH∞performance are obtained by means of elementary algebraic manipulations. These bounds are new in continuous‐time filtering and discrete‐time one‐step ahead prediction. As for discrete‐time filtering, the paper provides new proofs that are alternative to existing derivations based on the Krein spaces formalism. In particular, some remarkableH∞robustness properties of Kalman filters and predictors are highlighted. The usefulness of these results for improving the estimator design under a mixedH2/H∞viewpoint is also discussed. The dualization of the analysis allows one to evaluate guaranteedH∞robustness bounds for state‐feedback regulators of systems affected by actuator disturbances. Copyright © 2001 John Wiley & Sons, Ltd.

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