On eigenvalue problem of singular control

The linear quadratic (LQ) problem in discrete domain is considered. Sometimes weighting matrix R is likely non-negative symmetrical singular matrix, so singular control problem may appear. The solution of the eigenvalue problem was proposed. The vector of singular control system is divided into two kinds of vector, namely the first control vector and second one, then Riccati algebraic equation is established in state subspace. The method for eigenvalue problem of singular control was given. The method gives up solution of traditional method, that the generalized eigenvalue problem first is solved, then Riccati equation is done. The advantage of the method is to avoid direct solution of dynamic problem.