Singular LQ problem for nonregular descriptor systems

In this paper, a singular linear quadratic (LQ) problem for non-regular descriptor systems is investigated. Under some general conditions, the optimal control and the optimal state of the LQ problem are given. The optimal control is synthesized as state feedback. All the finite eigenvalues of the closed-loop system are located on the left-half complex plane. The state of the closed-loop system has the least free entries.