TY - JOUR

T1 - A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations

AU - Chu, E. K.W.

AU - Fan, H. Y.

AU - Lin, W. W.

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2005/2/1

Y1 - 2005/2/1

N2 - Continuous-time algebraic Riccati equations (CAREs) can be transformed, à la Cayley, to discrete-time algebraic Riccati equations (DAREs). The efficient structure-preserving doubling algorithm (SDA) for DAREs, from [E.K.-W. Chu, H.-Y. Fan, W.-W. Lin, A structure-preserving doubling algorithm for periodic discrete-time algebraic Riccati equations, preprint 2002-28, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan, 2003; E.K.-W. Chu, H.-Y. Fan, W.-W. Lin, C.-S. Wang, A structure-preserving doubling algorithm for periodic discrete-time algebraic Riccati equations, preprint 2002-18, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan, 2003], can then be applied. In this paper, we develop the structure-preserving doubling algorithm from a new point of view and show its quadratic convergence under assumptions which are weaker than stabilizability and detectability, as well as practical issues involved in the application of the SDA to CAREs. A modified version of the SDA, developed for DAREs with a "doubly symmetric" structure, is also presented. Extensive numerical results show that our approach is efficient and competitive.

AB - Continuous-time algebraic Riccati equations (CAREs) can be transformed, à la Cayley, to discrete-time algebraic Riccati equations (DAREs). The efficient structure-preserving doubling algorithm (SDA) for DAREs, from [E.K.-W. Chu, H.-Y. Fan, W.-W. Lin, A structure-preserving doubling algorithm for periodic discrete-time algebraic Riccati equations, preprint 2002-28, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan, 2003; E.K.-W. Chu, H.-Y. Fan, W.-W. Lin, C.-S. Wang, A structure-preserving doubling algorithm for periodic discrete-time algebraic Riccati equations, preprint 2002-18, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan, 2003], can then be applied. In this paper, we develop the structure-preserving doubling algorithm from a new point of view and show its quadratic convergence under assumptions which are weaker than stabilizability and detectability, as well as practical issues involved in the application of the SDA to CAREs. A modified version of the SDA, developed for DAREs with a "doubly symmetric" structure, is also presented. Extensive numerical results show that our approach is efficient and competitive.

KW - Cayley transform

KW - Continuous-time algebraic Riccati equation

KW - Doubling algorithm

KW - Matrix sign function

KW - Structure-preserving

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U2 - 10.1016/j.laa.2004.10.010

DO - 10.1016/j.laa.2004.10.010

M3 - Article

AN - SCOPUS:11044235476

VL - 396

SP - 55

EP - 80

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -