Please use this identifier to cite or link to this item: https://doi.org/10.1137/050625035
Title: A numerical method for a generalized algebraic Riccati equation
Authors: Chu, D. 
Lin, W.-W.
Tan, R.C.E. 
Keywords: Eigenvalues
Extended imaginary axis
Generalized algebraic Riccati equation
Semistabilizing solution
Stable eigenspace
Issue Date: 2006
Source: Chu, D., Lin, W.-W., Tan, R.C.E. (2006). A numerical method for a generalized algebraic Riccati equation. SIAM Journal on Control and Optimization 45 (4) : 1222-1250. ScholarBank@NUS Repository. https://doi.org/10.1137/050625035
Abstract: In this paper we develop a numerical method for computing the semistabilizing solution of a generalized algebraic Riccati equation (GARE). The semistabilizing solution of such a GARE has been used to characterize the solvability of the (J, J′)-spectral factorization problem for general rational matrices which have poles and zeros on the extended imaginary axis. The main difficulty for solving such a GARE is that its associated skew-Hamiltonian/Hamiltonian pencil has eigenvalues on the extended imaginary axis; consequently, it is not clear which eigenspace of the associated skew-Hamiltonian/Hamiltonian pencil can characterize the desired semistabilizing solution; i.e., it is not clear which eigenvectors and principal vectors corresponding to the eigenvalues on the extended imaginary axis should be contained in the eigenspace that we wish to compute, and hence the well-known generalized eigenvalue approach for the classical algebraic Riccati equations cannot be directly employed for it. Our proposed method consists of computations of the eigendecomposition of the system pencil corresponding to the eigenvalues on the extended imaginary axis and the stable eigenspace of an augmented matrix pencil; hence, it is a generalization of the generalized eigenvalue approach for the classical algebraic Riccati equations. © 2006 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Control and Optimization
URI: http://scholarbank.nus.edu.sg/handle/10635/102721
ISSN: 03630129
DOI: 10.1137/050625035
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