Convergence rates of stochastic homogeneous systems

被引：7

作者：

Hoshino, Kenta ^{[1
]}

Nishimura, Yuki ^{[2
]}

Yamashita, Yuh ^{[3
]}

机构：

[1] Aoyama Gakuin Univ, 5-10-1 Fuchinobe, Sagamihara, Kanagawa, Japan

[2] Kagoshima Univ, 1-21-40 Korimoto, Kagoshima, Kagoshima, Japan

[3] Hokkaido Univ, N14W9, Sapporo, Hokkaido, Japan

来源：

SYSTEMS & CONTROL LETTERS | 2019年 / 124卷

基金：

日本学术振兴会;

关键词：

Stochastic control; Finite-time stability; Homogeneous systems; FINITE-TIME STABILITY; STABILIZATION; STABILIZABILITY;

D O I：

10.1016/j.sysconle.2018.11.013

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This study considers stochastic homogeneous systems and focuses on the relation between their homogeneity and the convergence rates. We give a definition of stochastic homogeneous systems with weighted dilations as an extension of deterministic homogeneous systems. We also introduce the stability properties, such as exponential, rational, and finite-time stability with respect to homogeneous norms. As a main result, we show that their homogeneous degrees imply the convergence rates of asymptotically stable systems. Based on the result, we also deal with the stabilization of stochastic homogeneous control systems. We provide a design method of homogeneous feedback laws with homogeneous control Lyapunov functions, which guarantees the convergence rates. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：33 / 39

页数：7

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