Singular LQ problem for nonregular singular systems

This paper is concerned with the singular LQ problem for nonregular singular systems with persistent disturbances. The full information feedback control method is employed to achieve the optimal control. Through investigating the LQ problem for standard state space systems with persistent disturbances, and by a series of equivalent transformations, some sufficient conditions for the unique existence of optimal control-state pair are derived. These conditions are all described unitedly with matrix rank equalities, and the optimal control-state pair can be explicitly formulated via just solving an algebraic Riccati equation and a matrix equation. Moreover, the closed-loop system are proved possessing the least free entries, and a necessary and sufficient condition for the dynamic part of state of the closed-loop system to be unique is given.