The dynamic behaviors of controlled systems substantially depend on
the allowable magnitude and change rate of the control efforts, which are
determined by size of the actuator and inertia of the driving mechanism.
The proposed controller design algorithm in this paper can take into account independently both the magnitude and rate constraints on actuator dynamics.The control law is constructed in terms of linear matrix inequalities. A suitable chosen set of initial state condition,satisfying the property of invariant set estab lished by a simple linear matrix inequality, can represent the desired set of tracking commands. By the application of satellite attitude control based on a simplified rotational model, the effectiveness of the proposed algorithm is verified through the achievable performance under specified constraints on the magnitude and rate of the control torque.The time response simulations confirm with the design algorithms. It is demonstrated that the allowable change rate must be well handled;otherwise, not only the designated performance level can not be fulfilled,but also even the stability can not be preserved.