A numerical algorithm for finding solution of sign-indefinite algebraic Riccati equations for general multiparameter singularly perturbed systems

In this paper, a computational algorithm for solving sign-indefinite general multiparameter algebraic Riccati equation (SIGMARE) that arises in the H∞ filtering problem is investigated. After establishing the asymptotic structure of the solution of the SIGMARE, in order to solve the SIGMARE, Newton's method and two fixed point algorithms are combined. As a result, the new iterative algorithm achieves the quadratic convergence property and succeeds in reducing the computing workspace dramatically. As another important feature, the convergence criteria for small parameters εi is derived for the first time. Moreover, it is shown that the uniqueness and positive semidefiniteness of the convergence solutions are guaranteed in the neighborhood of the initial conditions