The Hermite positive definite solution of a system of nonlinear matrix equations

The problem of solving the Hermite positive definite solution for the system of nonlinear matrix equations is studied. Firstly, the existence of the Hermite positive definite solution of the system of matrix equations is proven, and the range of values is given. An iterative method for solving the system of matrix equations is constructed, and its convergence is proved by the monotone bounded theorem. Furthermore, the perturbation analysis is discussed and the erturbation upper bound is derived. Finally, numerical examples are given to illustrate the effectiveness and feasibility of the proposed iterative method.