Event-triggered synchronization for multi-agent networked systems with time-varying coupling strength and non-differentiable delays

This study explores the synchronization tracking issue within nonlinear multi-agent networked systems featuring non-differentiable delay. Diverging from conventional approaches, the analysis removes the assumption of delay differentiability, allowing for a broader spectrum of delay patterns. Initially, this paper establishes the properties of a pertinent differential inequality in the context of non-differentiable delay, and subsequently, it lays out sufficient conditions ensuring the exponential convergence of the multi-agent networked systems. Then, some novel static and dynamic event-triggered control strategies are devised, integrating variable over time control gain to attain tracking agreement. These strategies encompass various existing control methodologies and offer enhanced adaptability in practical scenarios. Additionally, the proposed approaches effectively mitigate Zeno behavior. The effectiveness of the theoretical findings is corroborated through simulation examples.