Distributed sliding mode control for a class of impulsive uncertain delayed partial differential equations via sliding mode compensator approach

The distributed sliding mode control (SMC) method of delayed partial differential equations (PDEs)with information of periodical impulse and reaction–diffusion terms (RDTs) is discussed in the article. Firstly, by adopting the sliding mode compensator approach, the switching function including impulsive effects is constructed, which is continuous along the system states. The sliding motion equation is then derived, and its parameters depend on that of sliding mode compensator.Via the direct linear matrix inequality method(DLIM), the exponential stability of sliding motion is analyzed. The proposed distributed SMC strategy can eliminate the impulsive effects and drive the closed-loop state onto a specific sliding manifold in limited time. Finally, a numerical simulation is presented to certify the availability of the proposed scheme.