Sliding mode control for uncertain impulsive reaction–diffusion systems with state delay

This article discusses the sliding mode control problem for a kind of impulsive reaction–diffusion systems (RDSs) with state delay and time-varying disturbance. A novel sliding surface containing regulation terms is constructed. The designed sliding mode controller can remove the impulsive effects on RDSs and drive the closed-loop state trajectories onto the specified sliding surface in finite time. By means of Linear matrix inequalities, the robust exponential stability of sliding motion is studied. Finally, a numerical example is provided to verify the availability of our findings.