Randomized Asynchronous Recursions with a Sinusoidal Input

This study considers a randomized asynchronous form of the discrete time-invariant state-space models, in which only a random subset of the state variables is updated in each iteration. When the system has a single input in the form of a complex exponential, it is shown that the output signal still behaves like an exponential in a statistical sense. The study presents the necessary and sufficient condition that ensures the stability of a randomized asynchronous system, which does not necessarily require the stability of the state transition matrix.