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Solution of the $H\sb{\infty}$ optimal linear filtering problem for discrete-time systems. (English) Zbl 0712.93053
Summary: The solution of $\ell\sb 2$ (minimum variance) and $H\sb{\infty}$ estimation problems is considered using a polynomial systems approach. The results for the $\ell\sb 2$-filtering problem which corresponds with Wiener or Kalman filtering/prediction, are first presented in polynomial matrix form. Attention then turns to the solution of the $H\sb{\infty}$ estimation problem for scalar systems. Numerous examples are presented to illustrate the computational procedures. The two types of estimator are appropriate to very different estimation problems and the new $H\sb{\infty}$ devices should be valuable in certain application areas.

93E11Filtering in stochastic control
93C55Discrete-time control systems
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