This paper systematically establishes criteria for ensuring $r$-th moment asymptotic stability and $r$-th moment exponential stability in stochastic systems via an event-triggered impulsive control (ETIC) strategy, considering both scenarios with and without impulsive delay. By constructing appropriate Lyapunov functions and applying stochastic analysis methods, the intrinsic relationships among event-triggered parameters, impulsive control (IC) strength, and system stability are established. Moreover, this paper thoroughly investigates how the selection of event-triggered parameters, the length of the inspection interval, and the magnitude of impulsive delay influence the convergence rate of the system. Finally, two numerical examples are presented to verify the effectiveness of the proposed ETIC method, one of which focuses on the consensus problem of stochastic multi-agent systems.

This paper explores multimode function multistability of Cohen-Grossberg neural networks (CGNNs) with Gaussian activation functions and mixed time delays. We start by using the geometrical properties of Gaussian functions. The state space is partitioned into $3^{\mu }$ subspaces, where $0\le \mu \le n$. Moreover, through the utilization of Brouwer's fixed point theorem and contraction mapping, some sufficient conditions are acquired to ensure the existence of precisely $3^{\mu }$ equilibria for $n$-dimensional CGNNs. Meanwhile, there are $2^{\mu }$ and $3^{\mu }-2^{\mu }$ multimode function stable and unstable equilibrium points, respectively. Ultimately, two illustrative examples are provided to confirm the efficacy of theoretical results.

This article investigates the stability problem of impulsive stochastic switched systems with double state-dependent delays. In the designed system, unstable and stable impulses are taken into consideration, respectively, and they do not need to function simultaneously with switching behavior. Additionally, two new ideas, i.e., mode-dependent switching density and mode-dependent impulsive density, are developed. Based on the Lyapunov function method and comparison principle, the asymptotic stability criteria for an impulsive stochastic switched system with state-dependent delays are given. Moreover, the application of theoretical results to neural networks and the neural network-based lecture skills assessment of normal students is analyzed. Finally, two numerical examples are provided to illustrate the effectiveness and reliability of the theoretical criteria.

This paper investigates the stability of a class of neutral highly nonlinear hybrid stochastic delayed systems with delayed impulses. Based on the comparison principle and stochastic analysis techniques, the lth moment asymptotic stability and the almost sure asymptotic stability of the argumented system are proven. Finally, the effectiveness of the theoretical results is demonstrated through two examples.

In this paper, the exponential input-to-state stabilization (EISS) problem for nonlinear systems subject to impulsive disturbance and continuous external inputs is addressed by an aperiodic intermittent control (APIC), which is further classified as either time-triggered APIC (TAPIC) or event-triggered APIC (EAPIC). To establish sufficient conditions for the realization of EISS, the Lyapunov approach is used. It is shown that the suggested APIC can successfully reduce the negative consequences of continuous external inputs and impulsive disturbance. Limiting the percentage of the active interval in the control procedure yields a range of impulse moments under TAPIC. The relationship among impulse disturbance, intermittent control parameters, the event-triggered mechanism (ETM), and the threshold is established under EAPIC to guarantee EISS. The predesigned ETM is used to generate a series of impulse disturbance moments. Furthermore, the Zeno phenomenon is excluded. Finally, an example of Chua's oscillator is presented to show how effective the system is under TAPIC and EAPIC.

This paper proposes a hybrid control strategy that combines aperiodic intermittent control (APIC) and event-triggered impulsive control (ETIMC) to study the finite-time stabilization (FTS) and finite-time convergence stabilization (FTCS) problems for nonlinear systems with partially known states. By applying the Lyapunov control criterion, linear matrix inequality (LMI) conditions, and dimension extension techniques, impulsive control gains based on partially known states are derived, and sufficient conditions to achieve FTS and FTCS are provided. Within the hybrid control framework, a close relationship between event-triggered parameters, intermittent control width, and boundary parameters is established, effectively avoiding the occurrence of Zeno-behavior. Finally, two numerical examples are presented to validate the effectiveness of the proposed hybrid control method.

This paper investigates input-to-state stability (ISS) of nonlinear systems with delayed impulse under event-triggered impulse control, where external inputs are different in continuous and impulse dynamics. First, an event-triggered mechanism (ETM) is proposed to avoid Zeno behavior. In order to ensure ISS of the considered system, the relationship among event triggering parameters, impulse intensity, and impulse delay is constructed. Then, as an application, ETM and impulse control gain for a specific kind of nonlinear systems are presented based on linear matrix inequalities (LMI). Finally, two examples confirm the feasibility and usefulness of the proposed strategy.

This paper studies the finite-time stabilization (FTS) and finite-time contraction stabilization (FTCS) of parameter-uncertain systems subjected to impulsive disturbances by using an event-triggered aperiodic intermittent control (EAPIC) method, which combines aperiodic intermittent control with event-triggered control. By employing the Lyapunov method and linear matrix inequality techniques, sufficient conditions for FTS and FTCS are derived. Additionally, within the finite-time control framework, relationships among impulsive disturbance, intermittent control parameters, and event-triggered mechanism (ETM) thresholds are established under EAPIC to ensure FTS and FTCS. The sequence of impulsive moments is determined by a predetermined ETM, and Zeno phenomena are also excluded. Finally, the effectiveness of the EAPIC approach is demonstrated through two numerical examples.

This paper discusses associative memories based on time-varying delayed fractional-order neural networks (DFNNs) with a type of piecewise nonlinear activation function from the perspective of multiple $\mathit{O}(t^{-\alpha })$ stability. Some sufficient conditions are gained to assure the existence of $5^n$ equilibria for $n$-neuron DFNNs with the proposed piecewise nonlinear activation functions. Additionally, the criteria ensure the existence of at least $3^n$ equilibria that are locally multiple $\mathit{O}(t^{-\alpha })$ stable. Furthermore, we apply these results to a more generic situation, revealing that DFNNs can attain $(2k+1{)}^n$ equilibria, and among them, $(k+1{)}^n$ equilibria are locally $\mathit{O}(t^{-\alpha })$ stable. Here, the parameter $k$ is highly dependent on the sinusoidal function frequency in the expanded activation functions. Such DFNNs are well-suited to synthesize high-capacity associative memories; the design process is given via singular value decomposition. Ultimately, four illustrative examples, including applying neurodynamic associative memory to the explaining-lesson skills assessment of normal students, are supplied to validate the efficacy of the results.

This paper investigates the stability problem of nonlinear stochastic systems with delayed impulses based on a self-triggered impulsive control (STIC) strategy. By employing the Lyapunov method, an explicit self-triggering mechanism (STM) with state-dependent waiting time parameters is designed, which ensures system stability while effectively avoiding Zeno behavior. Compared with traditional event-triggered impulsive control (ETIC) methods, this strategy does not require continuous state monitoring and can determine the next triggering instant based on the currently available state information. Furthermore, the developed theoretical results are applied to the STIC problem of nonlinear stochastic systems. Finally, the effectiveness and feasibility of the proposed method are validated through two numerical examples.