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.

In this research, we used an event-triggered impulsive control (ETIC) approach to study the Lyapunov stability of nonlinear systems subject to impulsive disturbances and impulse delays. Based on impulsive control theory, a novel event-triggering mechanism (ETM) that incorporates impulsive disturbance information was developed. The proposed ETM adopts an intermittent monitoring scheme, under which the impulsive control instants are autonomously dictated, ensuring that the controller is activated exactly once between two consecutive impulsive perturbations. As a result, the divergent dynamic behaviors induced by disturbances can be rapidly and effectively restrained. Furthermore, sufficient conditions were derived to exclude the occurrence of Zeno behavior and to guarantee the global asymptotic stability (GAS) of the closed-loop system under the ETIC framework. In addition, by utilizing linear matrix inequality (LMI) techniques, the synchronization of chaotic systems was successfully achieved. Theoretical analysis revealed that the stability of the system depends not only on the designed ETM but also on the presence of impulse delays. Finally, two numerical simulation examples were provided to demonstrate the effectiveness and feasibility of the proposed approach.