A. Lanzon, Y. Feng, B.D.O. Anderson, and M. Rotkowitz
Computing the Positive Stabilizing Solution to Algebraic Riccati Equations with an Indefinite Quadratic Term via a Recursive Method
IEEE Transactions on Automatic Control, vol. 53, no. 10, pp. 2280-2291, November 2008.

Abstract

An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.

Notes

There was a brief comment and response for this paper, but it just dealt with whether one of the examples we used could also be handled using another method.