Sliding mode synchronization of coupled hyperbolic–parabolic PDE systems subject to impulsive disturbances

At present, research efforts primarily concentrate on the dynamical behavior of dual-coupled hyperbolic–parabolic partial differential systems (HPPDS). In practical engineering applications, it is often the case that N HPPDS are coupled with each other. In this paper, the N coupled HPPDS with the impulsive disturbances is constructed and its synchronization problem is studied. Firstly, the definition of the N coupled HPPDS with impulsive disturbances is given. In the second stage, a synchronization scheme for the target system is developed using Lyapunov-based analysis and sliding mode control techniques. The construction of a sliding mode surface is followed by a proof of its reachability. Utilizing this surface, an appropriate sliding mode controller is designed to guarantee system stability, which leads to the synchronization of N coupled HPPDS. The validity and performance of the proposed approach are further demonstrated through simulation results.