Computing the Positive Stabilizing Solution to Algebraic Riccati Equations With an Indefinite Quadratic Term via a Recursive Method

Author

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

Author_Institution

Control Syst. Center, Univ. of Manchester, Manchester

Volume

53

Issue

10

fYear

2008

Firstpage

2280

Lastpage

2291

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.

Keywords

Riccati equations; convergence of numerical methods; game theory; iterative methods; matrix algebra; stability; Hamiltonian matrices; algebraic Riccati equations; game theoretic interpretation; global convergence; indefinite quadratic term; iterative algorithm; recursive method; Australia Council; Computational efficiency; Control systems; Convergence; Game theory; Iterative algorithms; Iterative methods; Packaging; Riccati equations; Symmetric matrices; $H_{infty}$ Riccati equations; Algebraic Riccati equation (ARE); indefinite quadratic term; iterative algorithms;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2008.2006108

Filename

4668534