Newton’s Method for Solving Riccati Equation Related to the Singularly Perturbed Systems

In this paper we present the algorithm for the algebraic Riccati equation with indefinite sign quadratic term for the singularly perturbed system by means of the Newton’s method. The proposed algorithm is very efficient from the numerical point of view because the algorithm is the quadratic convergence and the algebraic Riccati equation is solvable even if quadratic term is an indefinite sign. The main contributions of this paper are as follows. First, the sufficient condition corresponding to the perturbation parameter such that the proposed algorithm is quadratic convergence is presented. Second, the method which is based on the linear equations method for solving the algebraic Lyapunov equation of singularly perturbed system is given. In order to show the effectiveness of the proposed algorithms, a numerical example is included.