Periodic and event-based impulse control for linear stochastic systems with multiplicative noise

This paper studies the performance comparison of periodic and event-based sampling for a class of linear stochastic systems with multiplicative noise, where the impulse control is adopted. By solving boundary value problems, we obtain the analytic expressions of the mean sampling time and the average state variance under the event-based sampling. It is shown that the event-based impulse control has substantially smaller average state variance than the periodic control under the same sampling frequency. Particularly, for the integrator case, the performance ratio of the two sampling methods is given explicitly. By simulation, it is demonstrated that the advantage of event-based sampling over periodic sampling is most obvious for unstable systems, followed by critical stable systems, and least obvious for stable systems.