The paper studies the robust stability of linear uncertain systems under periodic event-triggered impulsive control (ETIC). Based on sliding variables, some sufficient conditions are derived to ensure the robust stability of the addressed impulsive control systems, and the effects of both external disturbance and uncertainty on the stability are revealed. Interestingly, it is verified that the proposed ETIC can ensure the robustness of the addressed systems with any bounded external disturbance. While, it is shown that the uncertainty may bring destabilizing impact to the stability. Further, compared with continuous event-triggered mechanism that often requires high hardware accuracy and sensor complexity in previous results, the proposed periodic event-triggered mechanism is more relaxed and realistic. It is also shown that the interevent time generated by the proposed periodic event-triggered mechanism has a unified positive lower bound, which cannot be derived by previous continuous event-triggered mechanism. Two illustrative examples are given to show the excellence of the main results. Note to Practitioners—It is known that the industrial plant emulator setup serves as a scaled-down representation of various industrial plant mechanisms, such as conveyor belts, drives, servomechanisms, and assembly machines. This paper is motivated by the problem of impulsive control for an industrial plant emulator setup, which has been studied by using continuous-time control or intermittent control in the previous results. Note that impulsive control only needs to implement at some discrete instants, which can reduce control cost and communication pressure compared with the continuous-time control and intermittent control. In this study, periodic ETIC, which contains the advantages of both periodic event-triggered control and impulsive control, is proposed to achieve the robust stability of linear multi-input uncertain systems with external disturbances. Some novel sliding-variables-based conditions have been obtained to guarantee the robust stability of addressed systems and the impacts of uncertainty and external disturbances on the stability are revealed simultaneously. It has been verified that the uncertainty may have destabilizing impact on the stability and under some conditions, the addressed periodic ETIC systems are robust with unknown bounded external disturbances. In addition, there exists a unified minimum time between arbitrary two consecutive triggered instants. In fact, the periodic ETIC can be also applied to some practical systems such as the second-order relay system and buck converter system, as these systems can be represented as linear uncertain systems with external disturbances. Furthermore, it is an intriguing future research topic to extend the derived results to the case of nonlinear systems.

This paper investigates the leader-following consensus of switched multi-agent systems under asynchronous control. This study uses the persistent dwell-time (PDT) method to characterize switching sequences, which can offer broader applicability than the average dwell-time method. This paper introduces a novel concept, average switching delay (ASD), to provide a global perspective on switching delays. Unlike previous literature, which often requires an upper bound on switching delays, ASD method effectively removes these constraints and provides the greater flexibility. Furthermore, we also investigate the potential impulse effects at the switching instants, as these can have a significant impact on system performance. The analysis demonstrates that when impulses satisfy specific conditions, they can facilitate the achievement of consensus in an initially inconsistent system. It is shown that, by using Lyapunov method, the relationship among the ASD, impulse gain, PDT coefficients and the system parameters is established, and some flexible consensus criteria of the switched multi-agent systems are derived. Finally, two numerical examples are given to demonstrate the validity of the results presented in this paper.

This article investigates the global exponential stability of the nonlinear delayed systems with logically selected impulses. First, the mathematical model for a new kind of hybrid systems is proposed. Based on the semi-tensor product of matrices, several sufficient conditions for globally exponential stability are derived. The impulsive switching signals are generated by two types of logical dynamical systems of addressed systems. To be specific, one signal is given in advance, and the other one is determined by some impulsive cycle sequences. An algorithm is developed to design logical dynamical systems for determining impulsive signals. The effectiveness of the main results is verified by two examples.

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

Event-triggering strategy is a control implementation technique which intends to minimizing resource usage while achieving the acceptable performance of the closed-loop system. In this paper, an event-triggered sliding mode control (SMC) is designed for attitude stabilization of a rigid spacecraft subject to external disturbances and model uncertainties. A semi-global event-triggering strategy is proposed for SMC to keep the system trajectory in the vicinity of a proposed sliding surface. Since in this sliding surface, the sliding mode is asymptotic stable, the trajectories of the attitude control system remain ultimately bounded under the circumstance of disturbances and uncertainties. Moreover, the given event-triggered control implementation is only dependent on the angular velocity at sampling instant and triggering strategy with Zeno phenomenon can be avoided. Some numerical simulations are shown to illustrate the availability of the obtained results.