Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises-Reference-Cited by-同舟云学术

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

Published:2023-12-15 Issue:11 Volume:59 Page:1550-1560
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Yurchenkov A. V.¹²,Belov I. R.¹

Affiliation:

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

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

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.

Publisher

The Russian Academy of Sciences

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