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Strict anisotropic norm bounded real lemma in terms of matrix inequalities. (English. Russian original) Zbl 1241.93050

Dokl. Math. 84, No. 3, 895-898 (2011); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 441, No. 3, 318-321 (2011).
Summary: This paper is aimed at extending the \(H _{\infty }\) Bounded Real Lemma to stochastic systems under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in the terms of information theory using the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the \(H _{\infty }\) norm. A state-space sufficient criterion for the anisotropic norm of a linear discrete time invariant system to be bounded by a given threshold value is derived. The resulting Strict Anisotropic Norm Bounded Real Lemma involves an inequality on the determinant of a positive definite matrix and a linear matrix inequality. These convex constraints can be approximated by two linear matrix inequalities.

MSC:

93E03 Stochastic systems in control theory (general)
93B36 \(H^\infty\)-control
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory

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