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Array algorithms for \(H^\infty\) estimation. (English) Zbl 0980.93077
This paper considers array algorithms for \(H^\infty\) filtering. These algorithms can be regarded as the Krein space generalizations of \(H^2\) array algorithms which are currently the preferred method for implementing \(H^2\) filters. The array algorithms considered include 2 main families, the square-root array algorithms, which are numerically more stable than others, and fast array algorithms, which, when the system is time-invariant, offer an order of magnitude reduction in the computational effort. In both cases, the explicit check for the positivity conditions required for the existence of \(H^\infty\) filters, is not necessary, because these conditions are built into the algorithms themselves.

93E10 Estimation and detection in stochastic control theory
93B36 \(H^\infty\)-control
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