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- Title
Stabilisation in distribution of hybrid ordinary differential equations by periodic noise.
- Authors
Bahar, Arifah; Dong, Ran; Mao, Xuerong
- Abstract
Many systems in the real world are periodic due to periodic phenomena in nature. Periodic hybrid stochastic differential equations are often used to model them. In many situations, it is inappropriate to study whether the solutions of periodic hybrid stochastic differential equations will converge to an equilibrium state (say, 0 or the trivial solution) but more appropriate to discuss whether the probability distributions of the solutions will converge to a stationary distribution, known as stability in distribution. This paper aims to determine whether or not a periodic stochastic state feedback control can make a given nonlinear periodic hybrid differential equation, which is not stable in distribution, to become stable in distribution. This problem will be referred to as stabilisation in distribution by periodic noise. There is little known on this problem so far. This paper initiates the study in this direction.
- Subjects
STOCHASTIC differential equations; STATE feedback (Feedback control systems); HYBRID systems; DIFFERENTIAL equations; DISTRIBUTION (Probability theory); ORDINARY differential equations; NOISE
- Publication
IET Control Theory & Applications (Wiley-Blackwell), 2023, Vol 17, Issue 4, p463
- ISSN
1751-8644
- Publication type
Article
- DOI
10.1049/cth2.12383