中文摘要：

针对一类含有时变时滞的不确定参数系统，研究了在执行器发生故障情况下系统指数稳定保代价可靠控制器设计问题。系统的性能函数是含有指数项和故障输入项的积分二次型函数。经过适当的状态变换，将原系统的指数稳定保代价可靠控制问题转化为另一个等价系统的保代价可靠控制问题。根据Lyapunov稳定性理论，得到了系统存在指数稳定保代价可靠控制器应满足的一个矩阵不等式，进一步将这个矩阵不等式转化为线性矩阵不等式（LMI），并给出了系统的保代价表达式。利用论文方法设计的控制器能够使得时滞系统对于任意允许的不确定量以及执行器故障都保持鲁棒可靠指数稳定，并且使系统具有保代价的性能指标。仿真结果表明了该控制器设计方法的有效性。

英文摘要：

The problem of guaranteed cost reliable control with exponential stabilization is investigated for time-varying delayed uncertain systems against actuator failures. The cost function of the systems is given in terms of the integral quadratic function including both index exponent and failure controls. By means of state variables transformation, the problem of guaranteed cost reliable control with exponential stabilization is re- duced to an equivalent problem of guaranteed cost reliable control. Based on Lyapunov stability theory, a sufficient condition for the existence of guaranteed cost reliable controller with exponential stabilization is derived and transformed to a linear matrix inequality （LMI）. The guaranteed cost controller then designed enables the closed—loop system to tolerate certain actuator failures and to retain exponential stability while to possess the performance index of guaranteed cost. The numerical example shows that the theoretical results are valid.