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.

In order to improve the utilization of computing or communication resources and reduce energy consumption, the study proposed the event-triggered impulsive observer-based output feedback control method for a class of nonlinear systems with aperiodic sampling and stochastic measurement noises. Firstly, by introducing an event-triggering mechanism that only depends on the discrete-time measurement output and an auxiliary variable, it designed a novel event-triggered impulsive observer. Then by constructing an augmented system composed of the original system and the observer error system and developing the quasi-periodic discretized Lyapunov function method, it established an ultimate bounded stability criterion in the mean square sense of the augmented closed-loop systems. The criterion reveals the influence mechanism of the sampling period, noise intensity, and event trigger parameters on system performance. Next, combined with the joint design approach, the output feedback controller synthesis problem was transformed into solving a set of LMIs based on the augmented system, thus solving the difficult problem that the state feedback gain and the observer gain cannot be separated in the presents of the stochastic measurement noise. Finally, on the Matlab platform, the performance of the proposed control method was analyzed via a connecting rod robotic arm. The experimental results demonstrate that the proposed method is effective in reducing the number of transmissions and conserving communication/computing resources. Furthermore, it successfully addresses the stabilization problems of nonlinear systems with stochastic measurement noise, thus confirming the effectiveness of the proposed approach.