Pahlajani, Chetan D.Chetan D.Pahlajani2025-08-302025-08-302017-03-0110.3934/dcdsb.20170272-s2.0-85011879291http://repository.iitgn.ac.in/handle/IITG2025/22521In this paper, we study the effect of small Brownian noise on a switching dynamical system which models a first-order dc/dc buck converter. The state vector of this system comprises a continuous component whose dynamics switch, based on the on/off configuration of the circuit, between two ordinary differential equations (ode), and a discrete component which keeps track of the on/off configurations. Assuming that the parameters and initial conditions of the unperturbed system have been tuned to yield a stable periodic orbit, we study the stochastic dynamics of this system when the forcing input in the on state is subject to small white noise fluctuations of size ϵ, 0 < ϵ ≪ 1. For the ensuing stochastic system whose dynamics switch at random times between a small noise stochastic differential equation (sde) and an ode, we prove a functional law of large numbers which states that in the limit of vanishing noise, the stochastic system converges to the underlying deterministic one on time horizons of order O(1/ϵ ^ν), 0 ≤ ν < 2/3.trueBuck converter | Functional law of large numbers | Stochastic differential equation | Switching dynamical systemArticlehttps://doi.org/10.3934/dcdsb.2017027569-584March 20170arJournal0WOS:000390100100016