中文摘要：

柔韧的稳定性；柔韧的滑动模式控制问题被使用与介绍一些松驰矩阵的一个新方法结合的参数依赖者 Lyapunov 功能的途径与 polytopic 类型不确定性为线性分布式的时间延期系统的一个类学习；调节参数，它能适当地被选择导致不太保守的结果。首先，一个足够的条件为自治系统的柔韧的稳定性被建议；下次，柔韧的稳定控制器的足够的条件；滑动模式的存在条件被开发。结果以线性矩阵不平等(LMI ) 被给，它能经由有效内部点的算法被解决。一个数字例子被举说明可行性；建议设计计划的优点。

英文摘要：

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.