Moment stability of pulse-width-modulated feedback systems subjected to random disturbances

We study the stability properties of pulse-width-modulated (PWM) feedback systems with stable plants, subjected to multiplicative and additive random disturbances (modeled by the derivative of a Wiener process). We show that when the parameters of the pulse-width modulator are within a computable range and the random disturbances are sufficiently small, then the PWM feedback system is globally asymptotically stable in the pth mean. We also show that in the presence of additive disturbances, such PWM feedback systems are bounded in the pth mean for arbitrarily large disturbances.