具有乘法噪声的时不变系统的各向异性规范的有界实数定理

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2023-12-29 DOI:10.1134/s00122661230110101

A. V. Yurchenkov, I. R. Belov

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引用次数: 0

摘要

摘要我们考虑一个离散时间不变系统，该系统在状态空间中具有乘法噪声。外源扰动选自非零色的时间不变遍历序列。我们认为外源扰动的平均各向异性水平受一个已知值的约束。我们通过求解带有特殊类型凸约束的矩阵不等式系统，得到了各向异性规范受给定数值约束的条件。演示了如何在所获条件的基础上构建静态状态控制，以确保该控制所包围系统的各向异性规范值最小。

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

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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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.