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Zbl 0934.93022
El Bouhtouri, A.; Hinrichsen, D.; Pritchard, A.J.
$H^\infty$-type control for discrete-time stochastic systems. (English)
[J] Int. J. Robust Nonlinear Control 9, No.13, 923-948 (1999). ISSN 1049-8923

An $H^{\infty}$-type theory is developed for linear stochastic systems with random state and input matrices which are subjected to stochastic disturbances and controlled by dynamic output feedback. A bounded real lemma is derived to apply a linear matrix inequality approach to the problem. Conditions for existence of a stabilizing controller reducing the norm of the perturbation operator to a level below a given threshold are derived. This generalizes the known results in the non-stochastic case.
[Michael Kohlmann (Bonn)]

MSC 2000:: *93B36 $H^\infty$-control
93C55 Discrete-time control systems
15A39 Linear inequalities

Keywords: stochastic systems; discrete time; multiplicative noise; $H^\infty$-control; bounded real lemma; linear matrix inequality

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Zentralblatt MATH Berlin [Germany]