Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations

Xuerong Mao, Wei Liu, Liangjian Hu, Qi Luo, Jianqiu Lu

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Abstract

Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao (2013) also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ . Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability.
Original languageEnglish
Pages (from-to)88-95
Number of pages8
JournalSystems and Control Letters
Volume73
Early online date20 Sep 2014
DOIs
Publication statusPublished - Nov 2014

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Feedback control
Differential equations
Stabilization
Asymptotic stability
Costs

Keywords

  • Brownian motion
  • Markov chain
  • mean-square exponential stability
  • feedback control
  • discrete-time state observation

Cite this

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abstract = "Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao (2013) also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ . Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability.",
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Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations. / Mao, Xuerong; Liu, Wei; Hu, Liangjian; Luo, Qi; Lu, Jianqiu.

In: Systems and Control Letters, Vol. 73, 11.2014, p. 88-95.

Research output: Contribution to journalArticle

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