An algorithm for the numerical solution of an important algebraic matrix equation in control system design

An algorithm for the numerical solution of an important algebraic matrix equation in control system design is developed. It is based on ideas arising from probability-1 homotopy methods, for the solution of algebraic systems of equations. The specialisation of this matrix equation into the algebraic Riccati matrix equation for continuous time systems is discussed. The proposed algorithm can be used to solve the optimal projection equations appearing in a reduced order compensator synthesis problem and in an anti-windup compensator synthesis problem. In addition, solutions to second order algebraic matrix polynomial equations are successfully obtained as solutions to special forms of the equation in question. Numerical examples show the advantage of the proposed method over other algorithms.