中文摘要：

基于比较原理，利用推广的向量Hanalay微分不等式，Dini导数，结合Green公式及不等式分析技术，研究一类具分布时滞的抛物型控制系统的变结构控制问题．首先对所导出的滑动模运动方程，在仅要求系数矩阵是个M-矩阵的条件下，获得了滑动模运动方程全局指数稳定性的充分条件，建立了滑动模运动方程全局指数稳定性定理．其次，设计了仅由状态函数描述的变结构控制器，给出了运动轨线到达滑动模态区的时间的估计．

英文摘要：

Based on comparison principle, the variable structure control problems for a class of parabolic type system with continuous distributed delays is investigated by using general vector Hanalay＇s differential inequality, Dini＇s derivative, Green formulation, and technique of inequality analysis. Firstly, only with M-matrix coefficient constraint, sufficient conditions are found for global exponential stability for the sliding mode equations with continuous distributed delays and several theorems of the global exponential stability for the sliding mode equations are established. Secondly, the variable structure controller of the system described only by state functions is designed, Furthermore, the length of time for motion trajectories to reach the sliding mode are estimated.