Periodic event-triggered asynchronous control for almost sure stabilization of hybrid stochastic systems with sampled measurements

In this paper, we were concerned with the periodic event-triggered asynchronous stabilization of a class of hybrid stochastic systems driven by continuous-time Markov chain and Brownian motion, where the measurements of state and mode were available only at sampling instants, and the control was diffusion-dependent. Static and dynamic periodic event-triggered control (PETC) strategies were proposed with a guaranteed minimum interevent time for every sample path solution. Different from the well-known input-to-state stability framework for stability and synthesis of event-triggered control systems, a comparison system approach was developed to show that if the hybrid stochastic system under continuous-time feedback control was $p$th-moment exponentially stable, then there existed a small sampling period and event-triggering parameters such that the resulting event-triggered control hybrid stochastic system was almost surely exponentially stable. Particularly, the proposed PETC strategies could integrate the beneficial impacts of stochastic noises, which distinguished them from previous results. Two numerical examples were provided to illustrate the efficiency of the theoretical results.