Pahlajani, Chetan D.Chetan D.Pahlajani2025-08-282025-08-282016-01-01https://d8.irins.org/handle/IITG2025/20020In 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 ?, 0<??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/??), 0??<2/3.en-USProbability (math.PR)Randomly perturbedSwitching dynamicsDC/DC convertere-Printe-Print123456789/555