In the practical control systems, the dynamic range of actuatiors is limited(or saturated) when actuators are driven by sufficiently large signals. This gives rise to a nonlinearity as a result of actuator saturation. For example, the upper limit is imposed on productive capability by available factory space and capital equipment. Other examples of those kinds of actuator saturations are a maximum torque of the actua- ting motors and a throttle position in an aircraft speed control A saturating actuator may lead not only to a large overshoot during start-up and shut-down, but also to deterioration of the performance due to the uncertainties. That is, the speed of response is decreased and, possibly, the system output may not follow the lalrge reference inputs. The large-overshoot may be accompanied by rest wind-up(or called by integra- tor wind-up) which comes from controllers with integral action in saturation operation regions. Eventually, as the overshoot increases, the system has a limit cycle or becomes oscillatorily unstable. Due to these cir- cumstances, many studies are focused on the stability and robustness of the nonlinear systems with satu- rating actuator in the time-domain as well as in the frequency-domain.