This paper investigates the issue of robust controller design for saturated linear systems, in which both the magnitude and rate constraints
on actuator dynamics are addressed. In the considered rotational satellite
system, the magnitude and rate saturations on the control torque are
prominent due to the limited power capacity and dynamic speed of the
thruster. Moreover, the control action needs to take into account the
parameter variation and uncertainty during system operation. In this work,
the time-varying uncertainty on system matrices in state-space representation is described in terms of norm-bounded conditions. By
augmenting suitable integral dynamics to the systems actuator, the control
effort of original plant is formulated as new state in the augmented
dynamics formulation and the input of the integrator is the rate of the
control efforts. The feedback gain is then designed to obtain suitable
actuator dynamics such that the desired performance can be optimized and the magnitude and rate constraints on actuator can be satisfied. The proposed robust output feedback control law is constructed in terms of linear matrix inequalities. The effectiveness of the proposed algorithm is verified by application to the example of satellite attitude control, in which the performance is minimized for varying specified constraints on the magnitude and rate of the control torque.