The Optimal Preview Control for a class of Descriptor Discrete-time Systems with Multirate Setting

The problem of optimal preview controller design for descriptor discrete-time systems with multirate setting is discussed in this paper. According to discrete-time lifting technique, the multirate preview control problem is transformed into the single-rate one for a certain augmented system. Then, an error system is constructed by using difference operator. Through employing some identities and including the difference of the known future information of desired tracking into the state vector of the error system, the problem is changed into optimal control problem of common descriptor system. Based on the result, a design method for an optimal preview controller is presented by the optimal control method of descriptor discrete-time systems. Moreover, the R-stabilizability and R-detectability of the error system have also been discussed.