Sliding mode control to stabilization of coupled time fractional parabolic PDEs subject to disturbances

Abstract In this article, the stabilization of coupled time fractional parabolic partial differential equations subject to external disturbances is investigated. By using sliding mode control method and backstepping approach, a boundary state feedback controller is designed to reject the matched disturbance and achieve the Mittag‐Leffler input‐to‐state stability of closed‐loop system. The existence of the generalized solution to the closed‐loop system is proven by Galerkin approximation scheme. Simulations are presented to illustrate the validity of our theoretical results.