This paper studies impulsive stochastic delay differential equations (ISDDE) with neutral terms, semi-Markov switching(SMS), and weakly restricted time-varying delays. By integrating a mode-dependent Lyapunov-Krasovskii functional with a novel measure-covering inequality for the delay term, we establish a unified master inequality that comprehensively incorporates the effects of continuous dynamics, neutral-state impulses, and random switching within a single framework. This formulation leads to explicit bounds in the p-th moment sense and establishes both mean and almost-sure exponential stability, with stability margins quantitatively characterized in terms of switching and impulse charges. In the context of recurrent neural networks (RNNs), the general criteria are specialized into tractable linear matrix inequality (LMI) conditions, which can be efficiently verified via standard semidefinite programming solvers. A reproducible parameter set and accompanying numerical simulations confirm the feasibility of the proposed approach, validate its sharpness, and demonstrate its practical utility.

In this article, we construct a state-feedback control strategy for the almost sure stability of stochastic nonholonomic semi-Markov jump systems. This work first introduces semi-Markov jump dynamics to stochastic nonholonomic systems. The dwell time depends on both the present and subsequent modes, significantly reducing conservatism in dwell time constraints. With the aid of a novel state transformation, the stochastic nonholonomic systems are decoupled. Based on stochastic analysis principles, the backstepping technique, and a multiple Lyapunov-like function framework, a novel controller is designed, and sufficient conditions are obtained to achieve almost sure stability via the state-feedback controller. In addition, by adopting the switching strategy, the phenomenon of uncontrollability is eliminated. Finally, an example demonstrates the effectiveness and feasibility of the proposed scheme.

This paper introduces a novel integrated control strategy synthesizing guaranteed cost control, H infinity control, and event-triggered control to mitigate the impact of stochastic cyber-attacks and external disturbances encountered during data transmission in multi-area power systems. The proposed strategy aims to enhance both the operational stability and economic efficiency of power systems. Within the designed control scheme, stochastic cyber-attacks and external disturbances are explicitly incorporated into the formulation of the system's control laws. Leveraging Gronwall's inequality, Lyapunov techniques, sufficient conditions are rigorously derived to guarantee performance for the cost control strategy. Furthermore, both event-triggered state feedback and output feedback controllers are designed, specifically, the output feedback controller employs a novel observer to address the issue of unmeasurable system states, enhancing its practical applicability for engineering implementations. Theoretical analysis demonstrates that the proposed scheme ensures finite-time bounded of the closed-loop system and guarantees an upper bound for the prescribed quadratic cost function. Numerical simulations substantiate the efficacy of the proposed approach.

This brief studies the finite-time control problem for a class of complex genetic regulatory networks (GRNs) with mixed time delays, actuator faults, and random disturbances. Firstly, different from existing Lyapunov-based methods, we propose a novel comparison principle approach to stability analysis, which avoids the construction of complex Lyapunov functionals. Secondly, by designing a fractional-power adaptive fault-tolerant controller, we achieve online compensation for actuator faults and suppression of disturbances without requiring prior knowledge of their bounds. Meanwhile, theoretical analysis shows that under relaxed conditions time delays need only be bounded, not differentiable, the closed-loop system states converge to zero exactly within a finite time T. Finally, simulations validate the effectiveness and superiority of the method.

This paper addresses the problem of almost surely asymptotic synchronization for stochastic delayed complex networks with Markovian switching (SDCNsMS). Leveraging complex information interactions among network nodes, we propose two categories of adaptive proportional-integral (PI) control protocols: node-based and edge-based (collectively termed NEAPIPs), accompanied by appropriate update laws. By integrating the LaSalle invariance principle, the stochastic Lyapunov function approach, and algebraic graph theory, we establish sufficient criteria guaranteeing almost surely asymptotic synchronization of SDCNsMS under the proposed adaptive PI control schemes. These criteria provide valuable guidance for designing practical engineering systems. Finally, numerical simulations are presented to validate the practical feasibility and effectiveness of the theoretical results.

A backpropagation neural network (BPNN) prediction method is designed for the predictive control of joint angles in pneumatic artificial muscles (PAMs) in this article, aimed at improving trajectory tracking accuracy for antagonistic joints. First, a backpropagation neural network model of pneumatic muscle antagonistic joints (PMAJs) is constructed based on the joint error angle and the error angular velocity. Second, the BPNN model is discretized to derive the backpropagation neural network prediction model for antagonistic joints. Subsequently, a backpropagation neural network-based prediction controller is designed to control the antagonistic joints, and the system's stability is demonstrated. Finally, the efficacy of the proposed algorithm is demonstrated through simulations and physical experiments in comparison with other algorithms. The results show that the BPNN model predictive control (BP NNMPC) can significantly improve trajectory tracking accuracy. The key innovation of this work lies in integrating a data-driven backpropagation neural network predictor into the model predictive control (MPC) framework, thereby enhancing the accuracy of the nonlinear muscle dynamics model. Compared with conventional MPC, the overall error rate of the BP NNMPC designed in this article is reduced by 40.5%.

This paper investigates the practical finite-time synchronization of fractional-order fuzzy neural networks subjected to output dead zones and quantization. To overcome the theoretical limitations of existing methods, we propose two major mathematical innovations: first, a novel class of fractional differential inequalities featuring a dual-power nonlinear structure (with exponents in (0,1] and [1, +infinity)) is established, which accurately captures the complex multistage convergence dynamics of fractional-order systems ; second, an advanced residual set estimation method is proposed to break the inherent conservatism of traditional approaches, rigorously proving that the synchronization residual set can be designed to be arbitrarily small without a strictly positive lower bound. On the control front, an output-based quantized controller is synthesized to jointly compensate for dead-zone limits and quantization errors without relying on full-state measurements, significantly enhancing its engineering feasibility. Finally, the theoretical framework is innovatively applied to a chaotic secure communication scheme. By explicitly embedding physical hardware constraints into the cryptographic model, the proposed scheme guarantees robust plaintext recovery in practical networked environments, which is thoroughly validated by numerical simulations.

This paper establishes novel stochastic finite-time stability (SFTS) criteria for stochastic nonlinear systems subject to delayed impulse effects. The proposed criteria are delay-dependent, explicitly quantifying how the SFTS property evolves with increasing time delay at impulse instants. To ensure SFTS in such systems, we derive the critical relationship between the impulse interval, impulse magnitude, and time delay. Furthermore, by constructing an appropriate Lyapunov function, we obtain conditions under which noise can induce finite-time stabilisation of an unstable deterministic nonlinear system with delayed impulses. Numerical examples are provided to validate the effectiveness and applicability of the proposed theoretical framework.

This study proposes a novel and cohesive framework to address stochastic finite-time consensus (FTC) problems, with the following main contributions: (i) We first introduce the original stochastic delay systems and, based on this, analyze the effects of Lévy noise, actuator faults, and Markov switching. Both leaderless and leader-follower topologies are considered, and a new control algorithm is proposed to investigate the fault-tolerant control problem under the influence of communication delays and Markov switching dynamics. (ii) To ensure that the states converge to a bounded compact set, the convergence analysis uses strong mathematical techniques, such as stopping time theory and the evolution of finite-time stochastic theory, to achieve mean-square and almost certain consensus. (iii) An important aspect of this study is the consideration of Markov-switching actuator faults, where fault occurrence and recovery evolve randomly according to a Markov process, introducing additional stochastic uncertainties into the system dynamics. Additionally, two numerical examples are provided to validate the correctness of the theoretical results.

This paper is committed to the stability analysis of discrete-time impulsive stochastic systems involving hybrid non-deterministic delays. We develop several novel criteria of weakly globally stochastically exponential stability for the suggested systems by means of delayed inequality approach under impulsive disturbance and Razumikhin method under impulsive control, respectively. It should be highlighted that different from the majority works that focused on constant delays or time-dependent delays, time delays in both the discrete-time stochastic system and the impulses are non-deterministic. Such delays should be handled with some new techniques, thus potentially leading to certain theoretical difficulties. In addition, the connection among the system state, impulses, hybrid non-deterministic delays is specifically provided and it sufficiently qualifies the positive or negative behaviours of impulses as well as delays. Finally, two numerical examples are presented to show the usefulness and the novelty of the derived results.

Impulsive stochastic systems, as classical hybrid systems, are prevalent across numerous scientific disciplines, attracting significant research interest in their stability characteristics. This paper investigates the input-to-state stability properties of impulsive stochastic systems featuring time varying or state-dependent delayed impulses within a two metrics framework. By applying the Lyapunov method, we establish sufficient criteria for input-to-state stability in impulsive stochastic systems, meeting the non-exponential Lyapunov function candidate and eventually uniformly bounded impulse frequency conditions. Importantly, these criteria do not require strict constraints on the size relationship between delays and impulse intervals; they encompass cases where the delay is shorter than the impulse interval and are also applicable when the delay exceeds the impulse interval. Our theoretical analysis highlights the distinct effects of stable and unstable delayed impulses on system stability, extending existing literature conclusions and theoretically demonstrating the robustness of the input-to-state stability property under the perturbation caused by uncertain impulse moments. Finally, the theoretical findings are applied to examples where existing methods are ineffective, and numerical simulations are presented to demonstrate the advantages of the new approach.

This paper investigates the existence, uniqueness, and Hyers-Ulam stability of a new class of higher-order coupled stochastic non-instantaneous impulsive Hilfer fractional switched differential equations with deviated arguments and Poisson jumps in finite-dimensional spaces. The well-posedness of the system is established using the method of integral contractors under suitable regularity assumptions and a weakened Lipschitz-type condition on the nonlinear operators. The proposed framework introduces a unified class of coupled Hilfer fractional stochastic switching systems that incorporates non-instantaneous impulses, switching dynamics, fractional integral initial conditions, and both continuous and jump-type stochastic perturbations. This structure provides a mathematically consistent and physically realistic model for hybrid dynamical systems with memory and random disturbances. The analysis employs techniques from fractional calculus, stochastic analysis, Laplace transforms, and Mittag-Leffler function theory. A numerical example and an application to electromechanical coupling and seeker stabilisation are presented to illustrate the effectiveness and practical relevance of the theoretical results.

This work reports design problem of the memory sampled-data (SD) controller for interval type-2 fuzzy singular systems (SSs) with external disturbances. First, an improved free-weighting matrix inequality is introduced for concerning fuzzy SSs to reduce conservatism of the integral terms. Then, a novel looped-functional-based Lyapunov-Krasovskii functional (LKF) is constructed that incorporates the data from sampling interval $\mathbf {z}(t)$ to $\mathbf {z}(t_{k})$ . With the help of improved integral inequality and novel LKF, a new set of admissibility conditions is developed in the form of linear matrix inequalities (LMIs). The developed criteria based on the memory SD controller ensure that the proposed systems is admissible with an $H_{\infty }$ attenuation level. Finally, numerical simulations are given to illustrate the usefulness and benefit of the proposed methods.

This paper investigates the secure optimal control problem (SOCP) for It & ocirc; stochastic Markov jump system (ISMJS) in the presence of unknown system dynamics, dynamic uncertainty, and denial-of-service (DoS) attacks. Initially, by utilizing the Lyapunov theorem, some sufficient conditions for achieving input-to-state stability (ISS) of the ISMJS are established. Subsequently, to overcome the inherent limitations of existing methods for solving the OCP, specifically, the requirement for both an initially stable control in policy iteration (PI) and the slow convergence rate of value iteration (VI), a model-based robust hybrid learning (HI) algorithm is first proposed. Although the algorithm effectively integrates PI and VI techniques to obtain optimal policies, the system dynamics are required during the learning process. Then, a model-free robust HI scheme without the system dynamics is developed to overcome the aforementioned challenges. Meanwhile, the stability and convergence of the proposed mechanisms are analyzed. Finally, the effectiveness and applicability of the proposed algorithms are validated through a simulation example involving a single-link robot arm. (c) 2025 Published by Elsevier Ltd.

In this article, we investigate the exponential stabilization of stochastic systems with sampled-data output. Two kinds of piecewise continuous functions (with/without noise) called intersample predictors are constructed to approximate discrete output signals. Corresponding predictor-based observers are then designed to obtain a good convergence of the estimation error. Based on the proposed predictors and observers, novel event-triggered strategies are developed to achieve exponential stabilization and address the asynchronism issue in input-output measurements. Finally, an illustrative example is provided to verify the effectiveness of the theoretical results.

This article aims to establish an averaging principle for conformable delay stochastic differential equations involving non-Lipschitz coefficients. First, we derive Duhamel's formula utilizing standard cosine family of linear operators. Subsequently, by virtue of Picard iteration technique and contradiction method, we demonstrate the existence and uniqueness of mild solution for the considered system, respectively. Then under suitable averaging conditions, we prove that the solutions to the original equations can be approximated by the solutions to the averaged equations both in the sense of mean square and probability. It means that Khasminskii classical approach can be extended to stochastic differential equations of conformable type. As verification, an example is provided to illustrate the theoretical results.

This paper explores the stability issue of stochastic McKean-Vlasov equations (SMVEs) through an innovative method: stabilization via stochastic delay feedback control with discrete observation. Unlike conventional techniques, this approach leverages historical states instead of solely relying on the current state, setting it apart from traditional stochastic feedback controls. The study examines how the diffusion term contributes to enhancing system stability despite the presence of random fluctuations and delays, guaranteeing both p-th moment exponential stability and almost sure exponential stability under a specific delay threshold S & lowast;. The primary contributions of this work include introducing a novel stability analysis framework utilizing stochastic delay feedback control, constructing Lyapunov functions that incorporate both state and distribution, and providing insights into asymptotic and moment exponential stability. Although identifying the optimal delay S & lowast; remains a practical challenge, the theoretical foundation laid in this study offers valuable guidance for real-world applications.

This paper focuses on high-order numerical methods for backward stochastic differential equations and proposes a novel one-step high-order scheme based on multi-stage predictor-corrector techniques. The proposed one-step high-order scheme integrates an initial prediction step with implicit multi-stage correction steps, offering the advantage of flexibly achieving adjustable high convergence orders through the number of stages while completing all necessary calculations within a single time step. Rigorous stability analysis of the proposed scheme is conducted to demonstrate that numerical errors remain bounded and do not grow exponentially with increasing time steps. Furthermore, strict error estimates are established via Itô-Taylor expansions to confirm the one-step high-order convergence property. Finally, numerical experiments on both linear and nonlinear backward stochastic differential equations validate the theoretical findings, showing good agreement between the theoretical convergence rates and practical results. Existing methods such as Euler schemes, θ -schemes, and other multi-stage schemes are shown to be special cases of the proposed framework.

In this paper, a novel stochastic finite-time stability (SFTS) criterion for stochastic nonlinear systems via intermittent feedback control is obtained based on the stochastic analysis techniques and the Lyapunov approach. In order to ensure SFTS for stochastic nonlinear systems via intermittent feedback control, the relationship between control interval, the parameter of the stochastic systems and the derivative of the Lyapunov function is established. Moreover, under certain conditions, the Brownian noise may play a positive role in the SFTS via intermittent feedback control. Meanwhile, we apply the main results to the SFTS via intermittent feedback control for a class of stochastic neural networks and then obtain some coefficient-type theorems. In addition, we have also obtained relevant conclusions on achieving stochastic fixed-time stability via intermittent control. Finally, several numerical examples are provided to demonstrate the effectiveness and applicability of the proposed theoretical framework.

This paper addresses the problem of stabilization in distribution for a class of nonlinear stochastic delay differential equations (SDDEs) driven by G-Brownian motion. A novel control scheme is proposed where a discrete-time state-feedback controller is applied at discrete sampling instants, as opposed to traditional continuous control, to reduce observation frequency and implementation cost. By constructing an appropriate G-Lyapunov functional, we derive conditions that guarantee the existence of a unique global solution and asymptotic stability in distribution for the closed-loop system. The model accounts for time-varying delays and nonlinear (polynomial) growth in the coefficients, broadening the scope of existing literature. To our knowledge, this is the first stabilization in distribution result for G-SDDEs via discrete-time control. These findings offer a theoretical foundation for developing low-cost control strategies under uncertainty.