Sliding mode control for a class of parabolic type systems with continuous distributed delay

The sliding mode control for a class of parabolic type systems with continuous distributed delay is investigated. By constructing auxiliary function and using matrix norm inequalities method, a memoryless sliding mode controller is designed and it drives the state trajectory of the system to the sliding manifold in finite time. Moreover, the global exponentially asymptotic stability for the sliding mode dynamic equation is analyzed. Experimental results show the simple structure and feasibility of the proposed controller.