The matrix bounds and fixed-point iteration for the solution of the discrete algebraic Riccati equation

In this paper, by constructing the equivalent form of the discrete algebraic Riccati equation (DARE), applying the eigenvalue inequalities of matrix's sum and product, we provide new lower and upper matrix bounds for the solution of the DARE, which improve some of the recent results. Further, using the derived matrix bounds and a fixed point theorem, we discuss the existence and uniqueness for the solution of the DARE. Finally, we give corresponding numerical examples to demonstrate the effectiveness of our results.