Event-triggered stabilisation and robust stability of stochastic differential equations

Tools

Liu, Zhijun and Mao, Xuerong (2025) Event-triggered stabilisation and robust stability of stochastic differential equations. IEEE Transactions on Automatic Control, 71 (1). pp. 660-667. ISSN 0018-9286 (https://doi.org/10.1109/TAC.2025.3598676)

[thumbnail of Liu-Mao-IEEE-TAC-2025-Event-triggered-stabilisation-and-robust-stabilityof-stochastic]
Preview
 Text. Filename: Liu-Mao-IEEE-TAC-2025-Event-triggered-stabilisation-and-robust-stabilityof-stochastic.pdf
Accepted Author Manuscript
License: Creative Commons Attribution 4.0 logo
Download (948kB)| Preview

Abstract

Influenced by the pioneering work of Astrom and Bernhardsson (2002), many results on the event-triggered control have been reported for different types of systems, such as ordinary differential equations (ODEs) and stochastic differential equations (SDEs). In the area of SDEs, the event-triggered mechanisms are essentially divided into two categories: (i) a mechanism is designed based on a criterion in terms of the mathematical expectation of the system state; (ii) it is designed based on a trajectory of the state observations. Both mechanisms have their own right. Our paper is concerned with (ii). We will set up a new event-triggered mechanism in category (ii) which differs from those in the existing papers. It is due to the new event-triggered mechanism that we will be able to develop a novel approach which is completely different from those in the existing papers. Our approach is to relate the event-triggered controlled SDE to the corresponding uncertain SDE. Our result shows that if the uncertain SDE is exponentially stable in pth moment for some p > 0, we can then make the event-triggered controlled SDE to be exponentially stable too. It is first time that the eventtriggered controlled SDE is related together with the uncertain SDE so that the techniques developed in the area of uncertain SDEs can be applied to the study of the event-triggered controlled SDEs. This is the key contribution in this paper.

ORCID iDs

Liu, Zhijun and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)