Advances in stabilisation of highly nonlinear hybrid delay systems

Dong, Hailing and Mao, Xuerong (2021) Advances in stabilisation of highly nonlinear hybrid delay systems. Automatica. ISSN 0005-1098 (In Press)

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Abstract

Given an unstable highly nonlinear hybrid stochastic differential delay equation (SDDE, also known as an SDDE with Markovian switching), can we design a delay feedback control to make the controlled hybrid SDDE become exponentially stable? Recent work by Li and Mao in 2020 gave a positive answer when the delay in the given SDDE is a positive constant. It is also noted that in their paper the time lag in the feedback control is another constant. However, time delay in a real-world system is often a variable of time while it is difficult to implement the feedback control in practice if the time lag involved is a strict constant. Mathematically speaking, the stabilization problem becomes much harder if these delays are time-varying, in particular, if they are not differentiable. The aim of this paper is to tackle the stabilization problem under non-differentiable time delays. One more new feature in this paper is that the feedback control function used is bounded.

ORCID iDs

Dong, Hailing and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:78430
    Dates:
    Date
    Event
    20 October 2021
    Published
    20 October 2021
    Accepted
    Keywords:Brownian motion, Markov chain, hybrid SDDE, bounded feedback control, exponential stability, Lyapunov functional, Mathematics, Control and Systems Engineering, Electrical and Electronic Engineering
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 Nov 2021 16:26
    Last modified:01 Nov 2023 11:46
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/78430
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