Abstract: The problem of guaranteed cost reliable control with constraint of decay rate is investigated for time-varying delayed uncertain systems against actuator failure.In the considered systems，the parameters uncertainties satisfy generalized matching conditions, and the time-varying delay and its derivative are bounded.A general model of actuator failure is adopted.The cost function of the systems is given in terms of integral quadratic function including both index exponent and failure controls.By means of state variables transformation, the problem of guaranteed cost reliable control with constraint of decay rate is reduced 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 constraint of decay rate is derived and transformed to a Linear Matrix Inequality（LMI）.The guaranteed cost controller 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.

Key words: guaranteed cost reliable control, decay rate, uncertain system, time-varying delay, actuator failure, linear matrix inequality

摘要： 针对一类含有时变时滞的不确定参数线性系统，研究了在执行器发生故障情况下系统具有指定衰减度的保代价可靠控制器设计问题。系统中的参数不确定性满足广义匹配条件，时变时滞及其变化率有界，执行器失效采用增益故障模型。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，将原系统的指定衰减度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，得到了系统存在指定衰减度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指定衰减度保代价可靠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。

关键词: 保代价可靠控制, 衰减度, 不确定系统, 时变时滞, 执行器失效, 线性矩阵不等式