Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method

Alexander Lanzon; Yantao Feng; Brian D O Anderson; Michael Rotkowitz

doi:10.1109/TAC.2008.2006108

Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method

Alexander Lanzon, Yantao Feng, Brian D O Anderson, Michael Rotkowitz

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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. © 2008 IEEE.

Original language	English
Pages (from-to)	2280-2291
Number of pages	11
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2008.2006108
Publication status	Published - 2008

Keywords

Algebraic Riccati equation (ARE)
H∞ Riccati equations
Indefinite quadratic term
Iterative algorithms

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title = "Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method",

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AB - 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. © 2008 IEEE.

KW - Algebraic Riccati equation (ARE)

KW - H∞ Riccati equations

KW - Indefinite quadratic term

KW - Iterative algorithms

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DO - 10.1109/TAC.2008.2006108

M3 - Article

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JO - IEEE Transactions on Automatic Control

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ER -

Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method

Abstract

Keywords

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