This paper addresses the challenges of designing reliable \(H_{\infty } \) filters for nonlinear networked control systems characterized by time-varying delays, probabilistic sensor faults, and communication constraints. Focusing on Takagi–Sugeno (T–S) fuzzy Markov jump systems (MJSs), we propose a \(H_{\infty } \) filtering framework that integrates sensor faults modeled as probabilistic failures and network-induced delays. In contrast to traditional continuous monitoring approaches, this research introduces a distinct event-triggered scheme to the networked control systems. This scheme offers notable advantages over existing methods by transmitting sensor data only when the sampled plant measurements breach a predefined event condition. The proposed delayed-state filter leverages fuzzy basis-dependent Lyapunov–Krasovskii functions (LKFs) with membership-dependent integral terms, effectively capturing time-varying delays and membership function dynamics to reduce conservatism. Stability conditions are formulated as linear matrix inequalities (LMIs), incorporating fuzzy basis-dependent Lyapunov matrices to enhance flexibility. Key contributions include (1) a generalized filtering error system modeling T–S fuzzy MJSs with multiple delays and event-triggered constraints. (2) Stability conditions formulated via LMIs with fuzzy basis-dependent Lyapunov matrices, significantly reducing conservatism compared to fixed Lyapunov methods. (3) Membership-dependent LKFs with fuzzy matrices in integral terms, improving delay-handling capabilities. Numerical simulations validate the framework’s efficacy, demonstrating enhanced stability.
