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\(H_{\infty}\) control and filtering of discrete-time stochastic systems with multiplicative noise. (English) Zbl 0989.93030
The paper examines linear discrete-time systems with stochastic uncertainties in state-space representations, and seeks an \(H^\infty\) type solution. The novelty in this paper, compared to prior contributions to the problem, is that here the optimization is considered on a finite horizon, thus, the end-point effect should be taken into account; in addition, the framework allows an output containing state dependent uncertainties. As tools, the paper develops a finite horizon version of the bounded real lemma, which is used in the analysis of a stochastic filtering via the adjoint system. A concrete example accompanies the abstract developments.

MSC:
93B36 \(H^\infty\)-control
93C55 Discrete-time control/observation systems
93E11 Filtering in stochastic control theory
93E24 Least squares and related methods for stochastic control systems
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