Reduced-Order Fault Estimator Design for Semi-Markov Jump Neural Networks Under the Weighted Try-Once-Discard Protocol

The actuator-fault estimation problem is addressed for discrete-time semi-Markov jump neural networks subject to time-varying delays, external disturbances, and communication constraints induced by the weighted try-once-discard (WTOD) protocol. Under this protocol, only the measurement channel with the largest weighted error is transmitted at each sampling instant, while the unselected channels retain their previously stored measurements at the filter side. To estimate the actuator fault, a fault-weighting dynamic system is first introduced. Then, by incorporating the WTOD-induced held measurement into the state vector, an augmented estimation model is constructed to describe the fault-weighting dynamics and the protocol-induced data-holding behavior within a unified framework. Based on this model, a mode-dependent and channel-dependent reduced-order fault-estimation filter is designed. The distinctive feature of the proposed framework is that the reconstruction of selected state components and the estimation of the actuator fault are addressed within a unified reduced-order estimator whose parameters depend jointly on the semi-Markov mode and the active WTOD transmission channel. By employing a Lyapunov–Krasovskii functional and using the semi-Markov transition information together with the WTOD scheduling constraint, sufficient LMI-based conditions are derived to ensure mean-square exponential stability and strict (T1,T2,T3)−δ dissipativity performance of the resulting estimation error system. Finally, two examples are provided to illustrate the numerical effectiveness of the proposed actuator-fault estimation method under different semi-Markov switching realizations.