A variable structure control method study for time-delay and uncertain system

The variable structure control problem is considered for a class of time-delay and uncertain system. The special switching function is designed by constructing the dynamic compensator, which can reduce the effect of the time-delay term and uncertainty for the system. The parameter of the switching function is constructed by using the matrix inequality and system transformation technique. Because the parameters in the criterion are solved by the linear matrix inequality, but not eatimated in the previous, which reduces the conservation in the conclusion. At last, an illustrative example is presented, the linear matrix inequality can be solved easily by using the LMI toolbox of Matlab which can show the new sliding mode condition not only restrains the quiver, but also makes the system has good character.