The paper deals with structured state feedback controllers design for linear time invariant (LTI) singular systems. New necessary and sufficient conditions for the existence of a structured state feedback guaranteeing the descriptor closed loop system admissibility is proposed by dint of linear quadratic (LQ) control theory. These conditions are presented in the form a system of matrix equations involving a non-smooth unconstrained equation. Keeping that in mind, the computation of the Clarke Jacobian of real symmetric matrix projection on semi-definite positives matrices’ cone, is used in order to solve the resulting system of matrix equations. Hence, local convergence of such non-smooth Newton like algorithm is proved. Based on this some numerical examples are presented to show the applicability of the proposed method.