期刊
AUTOMATICA
卷 136, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2021.110086
关键词
Brownian motion; Markov chain; Hybrid SDDE; Bounded feedback control; Exponential stability; Lyapunov functional
资金
- Royal Society, UK [WM160014, NA160317]
- Newton Fund, UK [NA160317]
- Royal Society of Edinburgh, UK [RSE1832]
- Shanghai Administration of Foreign Experts Affairs, PR China [21WZ2503700]
- Natural Science Foundation of Guangdong, PR China [2020A1515010372]
This paper addresses the stabilization problem under non-differentiable time delays and solves it by designing a bounded feedback control method.
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. (C) 2021 Elsevier Ltd. All rights reserved.
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