中文摘要：

稳定性和机械系统的围住的海角是重要研究话题之一。在这糊一个干燥磨擦振荡器的最终的围住的海角，属于非光滑的机械系统，被建议一个控制器设计方法调查。第一，为有推迟的州的反馈的名字的系统的稳定性的一个足够的条件被构造 Lyapunov Krasovskii 功能导出。推迟的反馈获得矩阵被使用线性矩阵不平等方法计算。第二根据推迟的州的反馈，一个连续函数被 Lyapunov 重新设计设计保证磨擦振荡器系统的解决方案最终在全面控制下面被围住。而且，最终的界限能被选择适当参数在实践调整。因此导致磨擦的颤动或不稳定性能有效地被控制。数字结果证明建议方法是有效的。

英文摘要：

Abstract The stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated by proposing a controller design method. Firstly a sufficient condition of the stability for the nominal system with delayed state feedback is derived by constructing a Lyapunov-Krasovskii function. The delayed feedback gain matrix is calculated by applying linear matrix inequality method. Secondly on the basis of the delayed state feedback, a continuous function is designed by Lyapunov redesign to ensure that the solutions of the friction oscillator system are ultimately bounded under the overall control. Moreover, the ultimate bound can be adjusted in practice by choosing appropriate parameter. Accordingly friction-induced vibration or instability can be controlled effectively. Numerical results show that the pro- posed method is valid.