Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems

By constructing an objective function and using the gradient search, a gradient-based iteration is established for solving the coupled matrix equations A(i)XB(i)=F-i, i=1, 2, ..., p. The authors prove that the gradient solution is convergent for any initial values. By analysing the spectral radius of the iterative matrix, the authors obtain an optimal convergence factor. An example is provided to illustrate the effectiveness of the proposed algorithm and to testify the conclusions established in this study.