The stability and boundedness of mechanical sys-tem have been one of important research topics.In this paperultimate boundedness of a dry friction oscillator,belongingto nonsmooth mechanical system,is investigated by propos-ing a controller design method.Firstly a sufficient conditionof the stability for the nominal system with delayed statefeedback is derived by constructing a Lyapunov-Krasovskiifunction.The delayed feedback gain matrix is calculated byapplying linear matrix inequality method.Secondly on thebasis of the delayed state feedback,a continuous functionis designed by Lyapunov redesign to ensure that the solu-tions of the friction oscillator system are ultimately boundedunder the overall control.Moreover,the ultimate bound canbe adjusted in practice by choosing appropriate parameter.Accordingly friction-induced vibration or instability can becontrolled effectively.Numerical results show that the pro-posed method is valid. The stability and boundedness of mechanical sys-tem have been one of important research topics. In this paperultimate boundedness of a dry friction oscillator, belongingto nonsmooth mechanical system, is investigated by propos- ing a controller design method. Firstly a sufficient conditionof the stability for the nominal system with delayed statefeedback is derived by constructing a Lyapunov-Krasovskiifunction. The delayed feedback gain matrix is ​​calculated byapplying linear matrix inequality method. Secondarily on thebasis of the delayed state feedback, a continuous functionis designed by Lyapunov redesign to ensure that the solu- tions of the friction oscillator system are ultimately boundedunder the overall control. More than, the ultimate bound canbe adjusted in practice by choosing an appropriate parameter. Accumatically friction-induced vibration or instability can becontrolled effectively.Numerical results show that the pro-posed method is valid.