Stabilisation in distribution of hybrid ordinary differential equations by periodic noise

Bahar, Arifah and Dong, Ran and Mao, Xuerong (2022) Stabilisation in distribution of hybrid ordinary differential equations by periodic noise. IET Control Theory and Applications. ISSN 1751-8644 (In Press)

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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. We will refer to this problem as stabilisation in distribution by periodic noise. There is little known on this problem so far. This paper initiates the study in this direction.

ORCID iDs

Bahar, Arifah, Dong, Ran and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)