Indefinite linear quadratic optimal control for discrete time-varying linear rectangular descriptor systems

In this article, the indefinite linear quadratic (LQ) optimal control problem for discrete time-varying rectangular descriptor systems is investigated, in which the indefinite weight matrices are considered in the quadratic cost function. With a suite of equivalent transformations, the indefinite LQ problem for discrete time-varying rectangular descriptor systems can be substituted by an equivalent indefinite LQ problem for standard state space systems. Then, the transformed equivalent indefinite LQ problem is solved by establishing a dual Krein space model, and the optimal control and optimal cost value are obtained by invoking the Kalman filter of Krein space. The form of state feedback optimal control corresponding to the original system is given. Next, to guarantee the dynamic part for the resulting optimal closed-loop system has a unique solution, some necessary and sufficient conditions are proposed. Finally, a numerical example is carried out to demonstrate the availability of established results.