The improved eigenvalue bounds for the solution of the discrete algebraic Riccati equation

In this paper, by using matrix eigenvalue inequalities and the properties of the positive definite solution for the discrete algebraic Riccati equation (DARE), we present upper and lower eigenvalue bounds for the solution of this equation. Moreover, applying majorization inequalities and eigenvalue summation (product) inequalities of special matrices, based on the derived results, we propose upper and lower bounds on eigenvalue summation and product for the solution of the DARE, which improve some of the recent results. The numerical examples show the effectiveness of the derived results.