In this paper we analyze an asymptotic stability of nonlinear singularly perturbed systems and propose a composite control with gain scheduling where the fast controller is the gain scheduled controller and the slow state plays a role of slowly varying parameters in gain scheduling. Specifically, the slow controller is designed by the slow manifold to stabilize the reduced slow system. As a result, the slow manifold of the system is the same as the designed manifold.

The main objective of vehicle suspensions is to improve ride comfort and road holding ability. Though passive suspensions consist of spring and damper, active suspensions adopt an actuator in addition to passive suspensions. In this paper, a quarter car model with an asymmetric hydraulic actuator is used. Moreover, the damping coefficient of the damper, which is changed according to the actuator velocity, is considered. The LPV (Linear Parameter Varying) model is obtained by applying feedback linearization technique. Next, a gain-scheduled controller, based on LQ regulator with different weighting factor, is designed according to the actuator velocity and the stability of the proposed controller is also proved. The effectiveness of the proposed controller is shown by numerical simulations.

Most of the previous controllers proposed for output regulation problems on uncertain nonlinear systems tried to keep the state variables to the nominal equilibrium points. In this letter, however, the dynamic state feedback controller makes the state variables follow the perturbed equilibrium points computed from an equilibrium-estimator.

This paper addresses output regulation for nonlinear systems driven by a time varying parameter. The derivative information of the time varying parameter is necessary for the improved regulation performance but it is not readily available in general. In this paper, we propose a velocity estimation of the time varying parameter for use in the control law without amplifying noise signals.