Stabilisation in distribution of hybrid systems by intermittent noise

Wei Mao, Junhao Hu, Xuerong Mao

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Abstract

For many stochastic hybrid systems in the real world, it is inappropriate to study if their solutions will converge to an equilibrium state (say, 0 by default) but more appropriate to discuss if the probability distributions of the solutions will converge to a stationary distribution. The former is known as the asymptotic stability of the equilibrium state while the latter the stability in distribution. This paper aims to determine whether or not a stochastic state feedback control can make a given nonlinear hybrid differential equation, which is not stable in distribution, to become stable in distribution. We will refer to this problem as stabilisation in distribution by noise or stochastic stabilisation in distribution. Although the stabilisation by noise in the sense of almost surely exponential stability of the equilibrium state has been well studied, there is little known on the stabilisation in distribution by noise. This paper initiates the study in this direction.
Original languageEnglish
Pages (from-to)4919-4924
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume68
Issue number8
Early online date26 Sept 2022
DOIs
Publication statusPublished - 31 Aug 2023

Keywords

  • nonlinear hybrid differential equation
  • intermittent noise
  • Brownian motion
  • Markov chain
  • stationary distribution
  • stabilisation

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