具有分布时滞不确定系统的滑模控制

摘要

针对一类含有分布时滞的不确定系统,通过利用Lyapunov稳定性理论和线性矩阵不等式方法进行滑模控制研究.首先,构造滑模控制器,使得系统满足滑模到达条件;其次,通过构造适当的Lyapunov泛函,给出闭环系统渐近稳定的充分条件.该充分条件通过采用虚拟反馈控制思想,结合状态反馈的极点配置方法,转换为线性矩阵不等式的形式,利用Matlab中的LMI工具箱进行求解.最后,仿真算例说明此方法的有效性.%Based on the Lyapunov stability theory and the linear matrix inequality approach, the sliding mode control for a class of uncertain systems with distributed delays is researched. Firstly,the sliding mode controller is constructed to satisfy the sliding mode reaching conditions. Secondly, the suffient conditions of closed-loop systems' asymptotical stability is given by constructing the appropriate Lyapunov functionals. In terms of virtual feedback control method and combinating pole assignment of state feedback, the suffient conditions can be shown in LMIs and sovled easily by LMI toolbox in Matlab. Finally, the simulation example is given to illustrate the validity of the method.