Memoryless Sliding Mode Controller Design for a Class of Parabolic Type Systems with Continuously Distributed Delays

The problem of sliding mode control is investigated for a class of parabolic type systems with continuously distributed delays.Firstly,by constructing auxiliary function and using matrix norm inequalities,a memoryless sliding mode controller is designed.Secondly,a sufficient condition of exponentially asymptotical stablility for the sliding mode dynamic equations is derived.Furthermore,the track time estimation from any initial state to sliding-model area is obtained.Simulation results demonstrate the effecteness of the proposed method.