INPUT-TO-STATE STABILITY OF INFINITE-DIMENSIONAL STOCHASTIC NONLINEAR SYSTEMS

Pengfei Wang; Mengyi Zhang; Huan Su

doi:10.3934/DCDSB.2021066

INPUT-TO-STATE STABILITY OF INFINITE-DIMENSIONAL STOCHASTIC NONLINEAR SYSTEMS

Pengfei Wang
, Mengyi Zhang
, Huan Su

Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, the input-to-state stability (ISS), stochastic-ISS (SISS) and integral-ISS (iISS) for mild solutions of infinite-dimensional stochastic nonlinear systems (IDSNS) are investigated, respectively. By constructing a class of Yosida strong solution approximating systems for IDSNS and using the infinite-dimensional version Itô’s formula, Lyapunov-based sufficient criteria are derived for ensuring ISS-type properties of IDSNS, which extend the existing corresponding results of infinite-dimensional deterministic systems. Moreover, two examples are presented to demonstrate the main results.

Original language	English
Pages (from-to)	821-836
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	27
Issue number	2
DOIs	https://doi.org/10.3934/DCDSB.2021066
State	Published - Feb 2022
Externally published	Yes

Keywords

Infinite-dimensional stochastic systems
Input-to-state stability
Itô’s formula
Lyapunov method
Mild solutions

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10.3934/DCDSB.2021066

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title = "INPUT-TO-STATE STABILITY OF INFINITE-DIMENSIONAL STOCHASTIC NONLINEAR SYSTEMS",

abstract = "In this paper, the input-to-state stability (ISS), stochastic-ISS (SISS) and integral-ISS (iISS) for mild solutions of infinite-dimensional stochastic nonlinear systems (IDSNS) are investigated, respectively. By constructing a class of Yosida strong solution approximating systems for IDSNS and using the infinite-dimensional version It{\^o}{\textquoteright}s formula, Lyapunov-based sufficient criteria are derived for ensuring ISS-type properties of IDSNS, which extend the existing corresponding results of infinite-dimensional deterministic systems. Moreover, two examples are presented to demonstrate the main results.",

keywords = "Infinite-dimensional stochastic systems, Input-to-state stability, It{\^o}{\textquoteright}s formula, Lyapunov method, Mild solutions",

author = "Pengfei Wang and Mengyi Zhang and Huan Su",

year = "2022",

month = feb,

doi = "10.3934/DCDSB.2021066",

language = "英语",

volume = "27",

pages = "821--836",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

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T1 - INPUT-TO-STATE STABILITY OF INFINITE-DIMENSIONAL STOCHASTIC NONLINEAR SYSTEMS

AU - Wang, Pengfei

AU - Zhang, Mengyi

AU - Su, Huan

PY - 2022/2

Y1 - 2022/2

N2 - In this paper, the input-to-state stability (ISS), stochastic-ISS (SISS) and integral-ISS (iISS) for mild solutions of infinite-dimensional stochastic nonlinear systems (IDSNS) are investigated, respectively. By constructing a class of Yosida strong solution approximating systems for IDSNS and using the infinite-dimensional version Itô’s formula, Lyapunov-based sufficient criteria are derived for ensuring ISS-type properties of IDSNS, which extend the existing corresponding results of infinite-dimensional deterministic systems. Moreover, two examples are presented to demonstrate the main results.

AB - In this paper, the input-to-state stability (ISS), stochastic-ISS (SISS) and integral-ISS (iISS) for mild solutions of infinite-dimensional stochastic nonlinear systems (IDSNS) are investigated, respectively. By constructing a class of Yosida strong solution approximating systems for IDSNS and using the infinite-dimensional version Itô’s formula, Lyapunov-based sufficient criteria are derived for ensuring ISS-type properties of IDSNS, which extend the existing corresponding results of infinite-dimensional deterministic systems. Moreover, two examples are presented to demonstrate the main results.

KW - Infinite-dimensional stochastic systems

KW - Input-to-state stability

KW - Itô’s formula

KW - Lyapunov method

KW - Mild solutions

UR - https://www.scopus.com/pages/publications/85123406920

U2 - 10.3934/DCDSB.2021066

DO - 10.3934/DCDSB.2021066

M3 - 文章

AN - SCOPUS:85123406920

SN - 1531-3492

VL - 27

SP - 821

EP - 836

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 2

ER -

INPUT-TO-STATE STABILITY OF INFINITE-DIMENSIONAL STOCHASTIC NONLINEAR SYSTEMS

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Keywords

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