基于LMI方法的一类时滞不确定系统的变结构控制

The Variable Structure Control for Uncertain Time-delay System Based on LMI Method

考虑了一类时滞不确定系统的变结构控制问题.通过构造动态补偿器,来设计一类特殊的切换函数,减少了时滞项和不确定性对系统的影响.利用矩阵不等式和系统变换技巧,给出了切换函数参数的具体构造,由于判据中需要的参数是由线性矩阵不等式解出的,不是事先估计选定的,减少了结论的保守性.最后给出了数例仿真,利用Matlab的LMI工具箱,能够方便的求出线性矩阵不等式,说明了用新的滑模到达条件不仅抑止了抖振,而且系统的运动具有良好的动态品质.

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 estimated in the previous, which reduce the conservation of the conclusion. At last, an illustrative example is presented, and the linear matrix inequality can be solved easily by using the LMI toolbox of Matlab, which shows the new sliding mode condition can not only restrain the quiver, then it can make the system have good character.