Journal
AUTOMATICA
Volume 112, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2019.108657
Keywords
Brownian motion; SDDE; Markov chain; Asymptotic stability; Lyapunov functional
Funding
- Royal Society, UK [WM160014]
- Royal Society, UK (Royal Society-Newton Advanced Fellowship) [NA160317]
- Newton Fund, UK (Royal Society-Newton Advanced Fellowship) [NA160317]
- EPSRC, UK [EP/K503174/1]
- National Natural Science Foundation of China [11971096]
- Natural Science Foundation of Jilin Province, PR China [20170101044JC]
- Education Department of Jilin Province, PR China [JJKH20170904kJ]
- Fundamental Research Funds for the Central Universities, PR China
Ask authors/readers for more resources
Given an unstable hybrid stochastic differential equation (SDDE, also known as an SDDE with Markovian switching), can we design a delay feedback control to make the controlled hybrid SDDE become asymptotically stable? If the feedback control is based on the current state, the stabilisation problem has been studied. However, there is little known when the feedback control is based on the past state. The problem becomes even harder when the coefficients of the underlying hybrid SDDE do not satisfy the linear growth condition (namely, the coefficients are highly nonlinear). The aim of this paper is to tackle the stabilisation problem for a given unstable highly nonlinear hybrid SDDE. (C) 2019 Elsevier Ltd. All rights reserved.
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