Event-Triggered Stabilization for Continuous-Time Stochastic Systems

This article addresses the event-triggered stabilization for continuous-time stochastic systems. Due to stochastic effects, the system state is hard to predict and dominate, and the system behavior would vary with every trial (i.e., sample path) even for the same initial condition. This gives rise to substantial challenges, especially, in determining the execution/sampling times and assessing the closed-loop performance, which urges us to develop powerful and sophisticated tools/methods for the analysis and design of stochastic event-triggered control. In this article, basic theorems, particularly a stochastic convergence theorem, are first proposed for stochastic event-triggered controlled systems. Then, a framework of event-triggered stabilization is established for the stochastic systems without applying the well-known Lyapunov theorems. Specifically, we present conditions under which event-triggered stabilization is feasible for the systems. Accordingly, static and dynamic event-triggering mechanisms are proposed with enforcing a fixed positive lower bound for the interexecution times. While avoiding infinitely fast execution/sampling, both asymptotic stabilization and exponential stabilization are achieved for the systems by the proposed stochastic convergence theorem. The involved analysis is helpful to form a pattern for stochastic event-triggered controlled systems. As the direct application of the established framework, the constructive design of event-triggered controller is realized, respectively, for two representative classes of stochastic systems.