Abstract-An iterative algorithm to solve Algebraic RiccatiEquations 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. Index Terms-Algebraic Riccati equation (ARE),Riccati equations, indefinite quadratic term, iterative algorithms.

In this paper, an iterative algorithm to solve Algebraic Riccati Equations (ARE) arising from, for example, a standard H ∞ control problem is proposed. By constructing two sequences of positive semidefinite matrices, we reduce an ARE with an indefinite quadratic term to a series of AREs with a negative semidefinite quadratic term which can be solved more easily by existing iterative methods (e.g. Kleinman algorithm in [2]). We prove that the proposed algorithm is globally convergent and has local quadratic rate of convergence. Numerical examples are provided to show that our algorithm has better numerical reliability when compared with some traditional algorithms (e.g. Schur method in [5]). Some proofs are omitted for brevity and will be published elsewhere.

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