Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems

Qianqian Zhang; Zhao Yan Li

doi:10.1109/CFASTA57821.2023.10243236

Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems

Qianqian Zhang^*
, Zhao Yan Li

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, the mean square exponential stability of a class of stochastic Stieltjes integral delay systems (SSIDSs) is studied. The basic properties and Lyapunov-Krasovskii (L-K) stability theorem with Stieltjes integrals of SSIDSs are discussed firstly. With the help of this theorem, a L-K functional with Stieltjes integrals is introduced to obtain a sufficient stability condition based on linear matrix inequalities (LMIs) by using multiple Jensen inequalities and the nature of stochastic integrals. The use of Stieltjes integrals allows to consider both discrete and distributed delays in the investigated equation. Finally, a numerical example is used to illustrate the effectiveness of the proposed methods.

Original language	English
Title of host publication	Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	18-23
Number of pages	6
ISBN (Electronic)	9798350332162
DOIs	https://doi.org/10.1109/CFASTA57821.2023.10243236
State	Published - 2023
Externally published	Yes
Event	2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 - Qingdao, China Duration: 14 Jul 2023 → 16 Jul 2023

Publication series

Name	Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

Conference

Conference	2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023
Country/Territory	China
City	Qingdao
Period	14/07/23 → 16/07/23

Keywords

Lyapunov-Krasovskii functionals
Stability
Stochastic Stieltjes integral delay systems

Access to Document

10.1109/CFASTA57821.2023.10243236

Cite this

Zhang, Q., & Li, Z. Y. (2023). Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems. In Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 (pp. 18-23). (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CFASTA57821.2023.10243236

Zhang, Qianqian ; Li, Zhao Yan. / Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems. Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. pp. 18-23 (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023).

@inproceedings{816f24e2600b48afbc76bcec763ceff6,

title = "Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems",

abstract = "In this paper, the mean square exponential stability of a class of stochastic Stieltjes integral delay systems (SSIDSs) is studied. The basic properties and Lyapunov-Krasovskii (L-K) stability theorem with Stieltjes integrals of SSIDSs are discussed firstly. With the help of this theorem, a L-K functional with Stieltjes integrals is introduced to obtain a sufficient stability condition based on linear matrix inequalities (LMIs) by using multiple Jensen inequalities and the nature of stochastic integrals. The use of Stieltjes integrals allows to consider both discrete and distributed delays in the investigated equation. Finally, a numerical example is used to illustrate the effectiveness of the proposed methods.",

keywords = "Lyapunov-Krasovskii functionals, Stability, Stochastic Stieltjes integral delay systems",

author = "Qianqian Zhang and Li, \{Zhao Yan\}",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 ; Conference date: 14-07-2023 Through 16-07-2023",

year = "2023",

doi = "10.1109/CFASTA57821.2023.10243236",

language = "英语",

series = "Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "18--23",

booktitle = "Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023",

address = "美国",

}

Zhang, Q & Li, ZY 2023, Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems. in Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023, Institute of Electrical and Electronics Engineers Inc., pp. 18-23, 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023, Qingdao, China, 14/07/23. https://doi.org/10.1109/CFASTA57821.2023.10243236

Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems. / Zhang, Qianqian; Li, Zhao Yan.
Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 18-23 (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems

AU - Zhang, Qianqian

AU - Li, Zhao Yan

PY - 2023

Y1 - 2023

N2 - In this paper, the mean square exponential stability of a class of stochastic Stieltjes integral delay systems (SSIDSs) is studied. The basic properties and Lyapunov-Krasovskii (L-K) stability theorem with Stieltjes integrals of SSIDSs are discussed firstly. With the help of this theorem, a L-K functional with Stieltjes integrals is introduced to obtain a sufficient stability condition based on linear matrix inequalities (LMIs) by using multiple Jensen inequalities and the nature of stochastic integrals. The use of Stieltjes integrals allows to consider both discrete and distributed delays in the investigated equation. Finally, a numerical example is used to illustrate the effectiveness of the proposed methods.

AB - In this paper, the mean square exponential stability of a class of stochastic Stieltjes integral delay systems (SSIDSs) is studied. The basic properties and Lyapunov-Krasovskii (L-K) stability theorem with Stieltjes integrals of SSIDSs are discussed firstly. With the help of this theorem, a L-K functional with Stieltjes integrals is introduced to obtain a sufficient stability condition based on linear matrix inequalities (LMIs) by using multiple Jensen inequalities and the nature of stochastic integrals. The use of Stieltjes integrals allows to consider both discrete and distributed delays in the investigated equation. Finally, a numerical example is used to illustrate the effectiveness of the proposed methods.

KW - Lyapunov-Krasovskii functionals

KW - Stability

KW - Stochastic Stieltjes integral delay systems

UR - https://www.scopus.com/pages/publications/85173625546

U2 - 10.1109/CFASTA57821.2023.10243236

DO - 10.1109/CFASTA57821.2023.10243236

M3 - 会议稿件

AN - SCOPUS:85173625546

T3 - Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

SP - 18

EP - 23

BT - Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

Y2 - 14 July 2023 through 16 July 2023

ER -

Zhang Q, Li ZY. Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems. In Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 18-23. (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023). doi: 10.1109/CFASTA57821.2023.10243236

Mean Square Exponential Stability of Stochastic Stieltjes Integral Delay Systems

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this