In this paper we propose a control law using a Lyapunov-like function that makes stable the systems which have mis-matched uncertainties. The existing control law using a Lyapunov-like function, which gives global saymptotic stability, is designed under the assumption of a targetsystem to be stable locally. But we broaden here the class of target systems by designing the control law which can give uniform ultimate boundedness to even the systems not satisfing the locally asymptotic stability. And we also show that the control law giving global asymptotic stability can be designed more systematically through using the uniform ultimate boundedness.