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

Shixian Luo; Linna Wei; Zi-Peng Wang; Shixian Luo; Linna Wei; Zi-Peng Wang

doi:10.3934/math.2025966

AIMS Mathematics

2025, Volume 10, Issue 9: 21737-21759. doi: 10.3934/math.2025966

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Research article

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

1.
School of Electrical Engineering, Guangxi University, Nanning 530004, China
2.
School of Mathematics and Information Science, Guangxi University, Nanning 530004, China
3.
School of Information Science and Technology, Beijing Laboratory of Smart Environmental Protection, Beijing University of Technology, Beijing 100124, China

Received: 07 July 2025 Revised: 28 August 2025 Accepted: 09 September 2025 Published: 18 September 2025
MSC : 93C10, 93D15

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.
- stochastic systems,
- event-triggered control,
- almost sure stability,
- stabilization by noise
Citation: Shixian Luo, Linna Wei, Zi-Peng Wang. Periodic event-triggered asynchronous control for almost sure stabilization of hybrid stochastic systems with sampled measurements[J]. AIMS Mathematics, 2025, 10(9): 21737-21759. doi: 10.3934/math.2025966

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Abstract

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.

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