Impulsive Observer-Based Fault-Tolerant Control for Singular PDE Systems: Application to Input–Output Control System

This article investigates impulsive fault-tolerant control for singular partial differential equation (PDE) systems subject to stochastic actuator failures. First, an impulsive observer is designed to estimate unmeasurable system states, which reduces the observation frequency while maintaining estimation accuracy, thereby effectively alleviating the computational burden and implementation challenges of complex dynamic systems. To capture potential stochastic actuator failures in engineering practice, a semi-Markov chain with a partially unknown kernel is then employed. Based on the measured outputs and estimated data, an impulsive controller is subsequently developed to stabilize the system. Furthermore, sufficient conditions for the admissibility of the singular PDE system are obtained by analyzing a Lyapunov function that incorporates discrete-time state information. Finally, the input–output control system between the petrochemical and the equipment manufacturing industries is characterized by a singular PDE system based on the Leontief dynamic input–output model, and the validity and effectiveness of the proposed control method are validated through a simulation.