Iterative Algorithm to Coupled Matrix Equations and Its Control Application

In order to solve the solution to the coupled Sylvester-conjugate transpose matrix equations, we present an iterative algorithm based on the hierarchical identification principle. For any initial values, the iterative solution consistently converges to the exact solution. Moreover, for any initial matrices, sufficient conditions are derived by means of a real representation of a complex matrix. Finally, In order to illustrate the efficiency of the proposed algorithm, control application to iterative algorithm has been presented.