TY - JOUR
T1 - A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations
AU - Hwang, T. M.
AU - Chu, E. K.W.
AU - Lin, W. W.
PY - 2005/9/20
Y1 - 2005/9/20
N2 - In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: ETXE = ATXA - (ATXB + CTS)(R + BTXB)-1(BTXA + STC) + C TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.
AB - In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: ETXE = ATXA - (ATXB + CTS)(R + BTXB)-1(BTXA + STC) + C TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.
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U2 - 10.1080/00207170500155827
DO - 10.1080/00207170500155827
M3 - Article
AN - SCOPUS:27844493643
VL - 78
SP - 1063
EP - 1075
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 14
ER -