Robust $H_{\infty}$ Stabilization for T-S Fuzzy Network Probabilistic Time-Delay Systems Using Periodic Memory Event-Triggered Network Control

This paper investigates the robust $H_{\infty}$ stabilization problem for Takagi-Sugeno (T-S) fuzzy network probabilistic time-delay systems with network-induced time-varying delays. To this end, a novel event-triggered strategy based on relative error is designed. Compared to traditional event-triggered strategies, this approach incorporates a buffer to effectively utilize known transmitted historical sampled data, which not only improves the system's dynamic process but also significantly reduces communication overhead. Subsequently, by comprehensively considering network-induced delays and the event-triggered scheme, a Piecewise Lyapunov functional is constructed. Through a series of Linear Matrix Inequalities (LMIs), the controller gains and event-triggered parameters are derived. Finally, the effectiveness of the proposed method is validated through simulation case studies.