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Finite-time \(H_\infty\) filtering for linear continuous time-varying systems with uncertain observations. (English) Zbl 1251.93049

Summary: We are concerned with the finite-time \(H_\infty\) filtering problem for linear continuous time-varying systems with uncertain observations and \(\mathcal L_{2}\)-norm bounded noise. The design of finite-time \(H_\infty\) filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time \(H_\infty\) filtering problem is solved. A numerical example is given to illustrate the performance of the \(H_\infty\) filter.

MSC:

93B36 \(H^\infty\)-control
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