Periodically intermittent control for stochastic nonlinear delay systems with dynamic event‐triggered mechanism

This paper is concerned with the stabilization problem for nonlinear stochastic delay systems with Markovian switching by feedback control based on discrete-time state and mode observations. By constructing an efficient Lyapunov functionals, we establish the sufficient stabilization criteria not only in the sense of exponential stability (both the mean-square stability and the almost sure stability) but also in other sense – that of stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is obtained. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With the aid of the delayed Mittag-Leffler matrix functions and the representation of solutions of these systems, we derive the controllability results as an application. By introducing a fractional delayed Gramian matrix, we provide sufficient and necessary criteria for the controllability of linear fractional stochastic delay systems. Furthermore, by employing Krasnoselskii’s fixed point theorem, we establish sufficient conditions for the controllability of nonlinear fractional stochastic delay systems. Finally, an example is given to illustrate the main results.

The 2025 9th International Conference on Mechanics, Mathematics and Applied Physics (ICMMAP 2025) was successfully held on-site at Harbin University of Science and Technology, Harbin, China, from December 12 to 14, 2025. The conference attracted approximately 200 participants, including researchers, engineers, and professionals from academia and industry, reflecting the growing interest and importance of mechanics, mathematics, and applied physics in both theoretical and practical domains. ICMMAP 2025 focused on interdisciplinary advances in mechanics, mathematical modeling, and applied physics. Key topics included optimization theory and algorithms, stochastic nonlinear systems, plasma physics, ionospheric perturbations, numerical methods for partial differential equations, and intelligent detection technologies. The conference provided a platform for sharing the latest research results, innovative methodologies, and practical engineering solutions across these fields. The conference featured keynote speeches delivered by distinguished experts from Uzbekistan, Russia, and China. Speakers included Prof. Bobomurat Ahmedov (Uzbekistan Academy of Sciences), Prof. Anatoly Kudryavtsev (Saint Petersburg State University / Harbin Institute of Technology), Prof. Wei Bian (Harbin Institute of Technology), Prof. Quanxin Zhu (Hunan Normal University), Prof. Chengxun Yuan (Harbin Institute of Technology), Prof. Qiang Zhang (Nanjing University), Assoc. Prof. Xiaozhou Li (University of Electronic Science and Technology of China), Assoc. Prof. Jia Li (Harbin Institute of Technology), and Dr. Fengyu Fu (Harbin University of Science and Technology). Their presentations covered frontier topics such as ionospheric perturbations, plasma-based electromagnetic wave amplification, sparse optimization problems, stabilization of stochastic nonlinear delay systems, plasma detection technologies, advanced numerical methods, and spectral analysis for parallel-in-time solvers. These keynote lectures offered valuable insights into both theoretical foundations and applied innovations. List of Committee Member is available in this PDF.

Computing the Density Function for a Nonlinear Stochastic Delay System

Fuzzy model-based control of nonlinear stochastic systems with time-delay

This paper focuses on the model of a class of nonlinear stochastic delay systems with Poisson jumps based on Lyapunov stability theory, stochastic analysis, and inequality technique. The existence and uniqueness of the adapted solution to such systems are proved by applying the fixed point theorem. By constructing a Lyapunov function and using Doob’s martingale inequality and Borel-Cantelli lemma, sufficient conditions are given to establish the exponential stability in the mean square of such systems, and we prove that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. The obtained results show that if stochastic systems is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic delay systems with Poisson jumps will remain exponentially stable, and time delay upper limit is solved by using the obtained results when the system is exponentially stable, and they are more easily verified and applied in practice.

Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points

The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as "continuous observation, intermittent action". Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.

In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With the aid of the delayed matrix functions of these systems, we derive the controllability results as an application. By using a delay Gramian matrix, we provide sufficient and necessary criteria for the controllability of linear stochastic delay systems. In addition, by employing Krasnoselskii’s fixed point theorem, we present some necessary criteria for the controllability of nonlinear stochastic delay systems. Our results improve and extend some existing ones. Finally, an example is given to illustrate the main results.

Finite-time stability of stochastic nonlinear delay systems with Markovian jumps and hybrid impulses

The 2022 2nd International Conference on Industrial Manufacturing and Structural Materials (IMSM 2022) was planned to be held on March 25-27, 2022 in Hangzhou, China. Due to the impact of COVID-19, many communities from all over the world were under strict health measures and strict travel restrictions, and participants of IMSM 2022 also meet with the difficulty of travel restrictions. According to the current epidemic prevention policy in Mainland China, our meeting was a virtual conference. IMSM is an annual conference which explored the development and implications in the related fields of Industrial Manufacturing and Structural Materials with an objective to present the novel and fundamental advancements. IMSM is to bring together innovative academics and industrial experts in the field of Industrial Manufacturing and Structural Materials to a common forum. The primary goal of the conference is to promote research and developmental activities industrial manufacturing and structural materials and another goal is to promote scientific information interchange between researchers, developers, engineers, students, and practitioners working all around the world. During the conference, the conference model was divided into three sessions, including oral presentations, keynote speeches, and online Q&A discussion. In the first part, some scholars, whose submissions were selected as the excellent papers, were given about 5-10 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 30-45 minutes to hold their speeches. In the second part, we invited two professors as our keynote speakers. Prof. Quanxin Zhu, Hunan Normal University, China, performed a speech: Stability and event-triggered control of stochastic nonlinear delay systems. And then we had Prof. Kamal Z. ZAMLI, Universiti Malaysia Pahang, Malaysia. Their insightful speeches had triggered heated discussion in the third session of the conference. Every participant praised this conference for disseminating useful and insightful knowledge. The proceedings are a compilation of the accepted papers and represent an interesting outcome of the conference. Topics include but are not limited to the following areas: Industrial Manufacturing Technology, Structural Materials and other related topics. All the papers have been through rigorous review and process to meet the requirements of international publication standard. We would like to acknowledge all of those who supported IMSM 2022. The help and contribution of each individual and institution was instrumental in the success of the conference. In particular, we would like to thank the organizing committee for its valuable inputs in shaping the conference program and reviewing the submitted papers. We sincerely hope that the IMSM 2022 turned out to be a forum for excellent discussions that enabled new ideas to come about, promoting collaborative research. We are sure that the proceedings will serve as an important research source of references and knowledge, which will lead to not only scientific and engineering findings but also new products and technologies. The Committee of IMSM 2022 Committee member are available in the pdf

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

The problem of robust stability and stabilization of stochastic large-scale delay systems has been investigated in recent years. However, the robust exponential stability and stabilization has not been considered. The purpose of this paper is to present delay-dependent criteria for robust decentralized exponential stabilization of the complex systems. The obtained results are based on algebraic Riccati equations and may be extended by using the widely-used LMI techniques.

SummaryThis paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches hmax, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.