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Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises

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Abstract

We consider a discrete-time-invariant system with multiplicative noise with implementation in the state space. The exogenous disturbance is chosen from the class of time-invariant ergodic sequences of nonzero colorness. We consider the level of mean anisotropy of the exogenous disturbance to be bounded by a known value. Conditions for the anisotropic norm to be bounded by a given number are obtained in terms of solving a matrix system of inequalities with a convex constraint of a special type. It is demonstrated how, on the basis of the obtained conditions, to construct a static state control that ensures the minimum value of the anisotropic norm of the system enclosed by this control.

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Funding

The work was carried out with partial support from the “Priority 2030” program of the Bauman Moscow State Technical University.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. V. Yurchenkov & I. R. Belov

  2. Bauman Moscow State Technical University, Moscow, 105005, Russia

    A. V. Yurchenkov

Authors
  1. A. V. Yurchenkov
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  2. I. R. Belov
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Correspondence to A. V. Yurchenkov or I. R. Belov.

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The authors of this work declare that they have no conflicts of interest.

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Yurchenkov, A.V., Belov, I.R. Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises. Diff Equat 59, 1557–1567 (2023). https://doi.org/10.1134/S00122661230110101

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  • DOI: https://doi.org/10.1134/S00122661230110101

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