Periodic Event-Triggered Impulsive Control of Linear Uncertain Systems

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.