Small-gain criteria for mean-square stability of random delay systems

Jianqi Chen; Junfeng Wu; Jie Chen

doi:10.1016/j.automatica.2024.111701

Small-gain criteria for mean-square stability of random delay systems

Jianqi Chen, Junfeng Wu, Jie Chen^*

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

2 Citations (Scopus)

Abstract

This paper studies stability problems of discrete-time linear time-invariant (LTI) systems subject to random time delays. Leveraging on a general mean-square, small-gain type stability condition for feedback systems containing structured stochastic multiplicative uncertainties, we derive mean-square small-gain stability conditions for LTI random delay systems, in which the delays may arise at random instants, or may have random delay lengths. We model the random delays as structured, correlated stochastic uncertainties and obtained necessary and sufficient mean-square stability criteria. The criteria require computing the spectral radius of a constant matrix, which enable us to ascertain whether a system's state variance matrix converges asymptotically despite the presence of random delays. © 2024 Elsevier Ltd

Original language	English
Article number	111701
Journal	Automatica
Volume	166
Online published	9 May 2024
DOIs	https://doi.org/10.1016/j.automatica.2024.111701
Publication status	Published - Aug 2024

Funding

This research is supported in part by the Hong Kong RGC under the grant numbers CityU 11203120 and CityU 11203321 and in part by the Shenzhen Science and Technology Program ( JCYJ20210324120011032 ), Shenzhen Institute of Artificial Intelligence and Robotics for Society .

Research Keywords

Mean-square stability
Random delay
Small-gain theorem
Structured correlated uncertainty

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10.1016/j.automatica.2024.111701

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title = "Small-gain criteria for mean-square stability of random delay systems",

abstract = "This paper studies stability problems of discrete-time linear time-invariant (LTI) systems subject to random time delays. Leveraging on a general mean-square, small-gain type stability condition for feedback systems containing structured stochastic multiplicative uncertainties, we derive mean-square small-gain stability conditions for LTI random delay systems, in which the delays may arise at random instants, or may have random delay lengths. We model the random delays as structured, correlated stochastic uncertainties and obtained necessary and sufficient mean-square stability criteria. The criteria require computing the spectral radius of a constant matrix, which enable us to ascertain whether a system's state variance matrix converges asymptotically despite the presence of random delays. {\textcopyright} 2024 Elsevier Ltd",

keywords = "Mean-square stability, Random delay, Small-gain theorem, Structured correlated uncertainty",

author = "Jianqi Chen and Junfeng Wu and Jie Chen",

year = "2024",

month = aug,

doi = "10.1016/j.automatica.2024.111701",

language = "English",

volume = "166",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Ltd.",

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TY - JOUR

T1 - Small-gain criteria for mean-square stability of random delay systems

AU - Chen, Jianqi

AU - Wu, Junfeng

AU - Chen, Jie

PY - 2024/8

Y1 - 2024/8

N2 - This paper studies stability problems of discrete-time linear time-invariant (LTI) systems subject to random time delays. Leveraging on a general mean-square, small-gain type stability condition for feedback systems containing structured stochastic multiplicative uncertainties, we derive mean-square small-gain stability conditions for LTI random delay systems, in which the delays may arise at random instants, or may have random delay lengths. We model the random delays as structured, correlated stochastic uncertainties and obtained necessary and sufficient mean-square stability criteria. The criteria require computing the spectral radius of a constant matrix, which enable us to ascertain whether a system's state variance matrix converges asymptotically despite the presence of random delays. © 2024 Elsevier Ltd

AB - This paper studies stability problems of discrete-time linear time-invariant (LTI) systems subject to random time delays. Leveraging on a general mean-square, small-gain type stability condition for feedback systems containing structured stochastic multiplicative uncertainties, we derive mean-square small-gain stability conditions for LTI random delay systems, in which the delays may arise at random instants, or may have random delay lengths. We model the random delays as structured, correlated stochastic uncertainties and obtained necessary and sufficient mean-square stability criteria. The criteria require computing the spectral radius of a constant matrix, which enable us to ascertain whether a system's state variance matrix converges asymptotically despite the presence of random delays. © 2024 Elsevier Ltd

KW - Mean-square stability

KW - Random delay

KW - Small-gain theorem

KW - Structured correlated uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85192288841&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85192288841&origin=recordpage

U2 - 10.1016/j.automatica.2024.111701

DO - 10.1016/j.automatica.2024.111701

M3 - RGC 21 - Publication in refereed journal

SN - 0005-1098

VL - 166

JO - Automatica

JF - Automatica

M1 - 111701

ER -

Small-gain criteria for mean-square stability of random delay systems

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GRF: Localization and Detection toward Securing Networked Control Systems

GRF: A Mean-square Analysis and Design Framework for Networked Control: Correlated Stochastic Multiplicative Uncertainties

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Small-gain criteria for mean-square stability of random delay systems

Abstract

Funding

Research Keywords

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GRF: Localization and Detection toward Securing Networked Control Systems

GRF: A Mean-square Analysis and Design Framework for Networked Control: Correlated Stochastic Multiplicative Uncertainties

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