Input-to-state stability of infinite-dimensional stochastic nonlinear systems

Pengfei Wang; Mengyi Zhang; Huan Su

doi:10.3934/dcdsb.2021066

Article Contents

2022, Volume 27, Issue 2: 821-836. Doi: 10.3934/dcdsb.2021066

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Input-to-state stability of infinite-dimensional stochastic nonlinear systems

Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, PR China

Received: July 2020

Revised: December 2020

Early access: March 2021

Published: February 2022

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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.

Keywords:

Infinite-dimensional stochastic systems,
mild solutions,
input-to-state stability,
Lyapunov method,
Itô's formula.

Mathematics Subject Classification: Primary: 37C75; Secondary: 60H15, 93D30.

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