A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.
Disturbance Attenuation for Constrained Discrete-Time Systems via Receding Horizon Controls