Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations

Surong You, Liangjian Hu, Jianqiu Lu, Xuerong Mao

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Abstract

This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.
Original languageEnglish
JournalIEEE Transactions on Automatic Control
Early online date27 Apr 2021
DOIs
Publication statusE-pub ahead of print - 27 Apr 2021

Keywords

  • Brownian motion
  • Markov chain
  • stability in distribution
  • delay feedback control

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