Event-Triggered Impulsive Control for Time-Varying Systems

This paper addresses the stability of time-varying systems using event-triggered impulsive control. A new event-triggered mechanism with time-varying structure is proposed, ensuring global asymptotic stability and avoiding Zeno behavior. The relationship between impulse actions, time delay, and system dynamics is explored, with two examples confirming the results. Note to Practitioners-The motivation of this paper is the challenge of stabilizing time-varying systems with reduced control efforts, which is a common issue in automation and control systems. Specifically, the paper introduces an event-triggered impulsive control (ETIC) approach to address this problem. The novelty of this work lies in the development of a new event-triggered mechanism (ETM) that incorporates a time-varying structure. This enables the system to use its own time-varying dynamics to trigger control actions, reducing the frequency of impulse actions compared to previous mechanisms. This leads to a reduction in control costs without compromising system stability. The proposed method guarantees global asymptotic stability (GAS) while preventing Zeno behavior, which can be problematic in traditional event-triggered systems. The practical benefits of this research extend to various automation applications, such as robotic control systems, where minimizing control actions while ensuring stability is critical for efficiency and cost reduction. For example, the method is demonstrated in a wheeled mobile robots velocity tracking. Future extensions of this work could explore its application in more complex systems, including those with multiple interacting subsystems or with real-time disturbances. This approach can be further refined to handle non-linear dynamics and stochastic disturbances, potentially expanding its applicability to a broader range of automated processes and systems in industrial and robotic settings.