Dual‐Channel Periodic Event‐Triggered Fault Estimation and Fault‐Tolerant Control for Singularly Perturbed Systems With Unknown Time‐Varying Delays

This paper investigates the problems of fault estimation (FE) and fault‐tolerant control (FTC) for a class of singularly perturbed systems (SPSs) affected by unknown time‐varying delays, external disturbances, and actuator faults in a network environment under dual‐channel dynamic periodic event‐triggered. To improve the communication efficiency of network channels, two different dynamic periodic event‐triggered mechanisms (ETMs) with transmission delays are developed between the sensor to observer and the observer to controller, respectively. Meanwhile, the Zeno behavior is excluded due to periodic sampling. To achieve simultaneous estimation of system states and fault signals while addressing the problem of unknown time‐varying state delays, a novel event‐triggered state/fault observer is proposed. Then, an event‐triggered fault‐tolerant controller is designed based on the estimated information of the system state and fault signal to ensure the stability of the closed‐loop system. According to Lyapunov‐Krasovskii theorem and the free‐weighting matrix technique, sufficient conditions for the stability of the observer and the controller are presented in the form of linear matrix inequalities (LMIs), where a ‐dependent Lyapunov function is considered. The results demonstrate that the proposed observer and controller design strategies can effectively suppress external disturbances and ensure satisfactory estimation accuracy, convergence speed, as well as steady‐state response of FTC when faults occur for all . Finally, the feasibility of the proposed design method is validated through numerical examples.