Array algorithms for \(H^\infty\) estimation. (English) Zbl 0980.93077

Hassibi, Babak; Kailath, Thomas; Sayed, Ali H.

IEEE Trans. Autom. Control 45, No. 4, 702-706 (2000).

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.

Reviewer: Klaus Ehemann (Karlsruhe)

MSC:

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

Keywords:

robustness; array algorithms; \(H^\infty\) filtering; square-root array algorithms; fast array algorithms