In the paper, we investigate the exponential stability of nonlinear delayed systems with destabilizing and stabilizing delayed impulses, respectively. Specifically, the study can be divided into tw...

In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive time-delay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid impulses, which contain both stabilizing impulses and destabilizing impulses. Three illustrative examples are presented to reveal the potential impacts of delay on the stability of impulsive control systems.

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.

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.

In the paper, the periodic event-triggered adaptive controller is proposed for attitude stabilization of a rigid spacecraft with model uncertainties, external disturbances, and input saturation. We adopt the periodic state measurement instead of the continuous one, and it is known that the former is more economical and practical than the latter due to the relaxation of continuous measurements. Moreover, new event-triggered adaptation update laws and the periodic event-triggering strategy are proposed for adaptive sliding mode control (SMC) to guarantee the states in the practical sliding mode. It is illustrated that the states of the attitude control system are ultimately bounded. Further, it is proved that the presented periodic event-triggered strategy is without Zeno phenomenon and there exists a uniform lower bound for each interevent time. Some numerical examples are given to demonstrate the validity of the derived control strategy.