Delayed impulsive stabilisation of discrete-time systems: a periodic event-triggering algorithm

Abstract

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals which are called event times. Sufficient conditions are established to guarantee asymptotic stability of the resulting impulsive systems. It is worth mentioning that the event times are different from the impulse times, that is, the control signals are updated at each event time but the actuator performs the impulsive control tasks at a later time due to time delays. The effectiveness of our theoretical result with the proposed scheme is illustrated by three examples.

Keywords:

• Discrete-time system
• time delay
• periodic event-triggered control
• impulsive control
• asymptotic stability

Acknowledgments

The authors are grateful to anonymous reviewers whose valuable comments helped improve the quality of this study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grants RGPIN-2020-03934 and RGPIN-2022-03144.