The solution bounds and fixed point iterative algorithm for the discrete coupled algebraic Riccati equation applied to automatic control

In this article, applying the special properties of nonnegative matrices and symmetric matrices, we consider the coupled term as a whole and derive the solution bounds of the discrete coupled algebraic Riccati equation. This reduces the error of taking apart the coupled term separately when applying inequality techniques to get the bounds in general. Then, using Cauchy-Schwarz inequality, matrix norm inequalities and a fixed point theorem, we discuss the existence uniqueness condition and fixed point iteration for the solution of this equation. Finally, we offer corresponding numerical examples to illustrate the effectiveness of our results.