TY - JOUR
T1 - Stabilisation in distribution of hybrid systems by intermittent noise
AU - Mao, Wei
AU - Hu, Junhao
AU - Mao, Xuerong
N1 - © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
PY - 2023/8/31
Y1 - 2023/8/31
N2 - 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.
AB - 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.
KW - nonlinear hybrid differential equation
KW - intermittent noise
KW - Brownian motion
KW - Markov chain
KW - stationary distribution
KW - stabilisation
UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
U2 - 10.1109/TAC.2022.3209370
DO - 10.1109/TAC.2022.3209370
M3 - Article
SN - 0018-9286
VL - 68
SP - 4919
EP - 4924
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 8
ER -