This article is cited in 6 papers

Linear Systems

Lemma on boundedness of anisotropic norm for systems with multiplicative noises under a noncentered disturbance

A. V. Yurchenkov<sup>ab

a</sup> Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
^b Bauman Moscow State Technical University, Moscow, 105005 Russia

Abstract: We consider a linear discrete time-varying system with multiplicative noise acted upon by colored exogenous disturbance with nonzero first moment. Multiplicative noises are modeled in the form of linear combinations of deterministic matrices with pairwise independent random coefficients. For this system, we describe a method, based on a state-space realization, for calculating the anisotropic norm in terms of Riccati equations.

Keywords: multiplicative noise, time-varying system, noncentered disturbance, anisotropy, anisotropic norm.

Presented by the member of Editorial Board: B. M. Miller

Received: 23.02.2020
Revised: 10.06.2020
Accepted: 09.07.2020

DOI: 10.31857/S0005231021010037

 English version: Automation and Remote Control, 2021, 82:1, 51–62

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