The sliding mode variable structure control for a class of interval distributed parameter systems with time-delay

The sliding mode control (SMC) problems are researched for a class of interval distributed parameter systems with time-delay. Firstly, this system is represented in the distributed parameter systems with parameter uncertainty, and a sufficient condition for robust asymptotically stable is obtained for the sliding mode by constructing Lyapunov functions, employing linear matrix inequality (LMI). Secondly, a variable structure control (VSC) law is designed, and, the time estimation is given on starting from the initial position of any sate trajectory curve to arrive sliding-model area. Finally, a numerical example is given, and the feasibility and effectiveness of this method is explained.