SOLVING SYSTEMS OF SECOND-ORDER MATRIX EQUATIONS

Анотація

Matrix equations and systems of matrix equations are widely used in control system optimization problems. However, there are developed only methods for solving the most popular matrix equations, like  Riccati and Lyapunov equations .There is no universal approach to solving all problems of this class. The previously considered method of solving systems of algebraic equations over a field of real numbers [1] is summarized in this paper and a scheme for systems of polynomial matrix equations of the second degree with many unknowns is proposed. Also, the recurrent formula for developing a solution into a chain matrix fraction is given. The convergence of the proposed method is investigated. The results of numerical experiments that confirm the validity of theoretical calculations and the effectiveness of the proposed scheme are presented.