Stabilization of Uncertain Parabolic PDE Systems Under Weighted Try-Once-Discard Protocol With Actuator Failures

This article investigates the output feedback stabilization problem for a parabolic partial differential equation (PDE) system with uncertain parameters, which is subject to limited communication resources. First, to alleviate the burden of channel communication and avert data collision, the multichannel measurement outputs are scheduled by the weighted try-once-discard protocol. Moreover, to bridge the gap between theory and reality, the Markov process is utilized to depict the occurrence of various actuator faults in a stochastic manner. An impulsive closed-loop model is established in light of the network-induced delay and various stochastically occurring actuator faults. Following the model, sufficient criteria for guaranteeing the input-to-state stability of the PDE system are put forward by constructing a new Lyapunov functional. Then, one can deduce the determination of the controller gains and weighted matrices by employing the technique of linearizing the matrix inequalities. Finally, simulation results unequivocally demonstrate the effectiveness of the proposed method.