On the Theory of Nonlinear Matrix Equation X s = Q + A H (I ⊗ X - C)- δ A

In this paper, the nonlinear matrix equation X s = Q±A H (I ⊗ X − C)− δ A are discussed. We present some necessary and sufficient conditions for the existence of a definite positive solution for this equation, and some related properties of the definite positive solution such as boundary.