Results 181 to 190 of about 1,417,876 (221)

The Stabilizing Solution of the Algebraic Riccati Equation

SIAM Journal on Control, 1973
This paper investigates solutions $\hat X$ of the algebraic Riccati equation $F'X + XF - XGG'X + Q = 0$ with the property $\operatorname{Re} \lambda (F - GG'\hat X) \leqq 0$. The uniqueness and existence of such a solution is completely characterized.
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A Numerical Method for a Generalized Algebraic Riccati Equation

SIAM Journal on Control and Optimization, 2006
Summary: 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 \((J, J^\prime)\)-spectral factorization problem for general rational matrices which have poles and zeros on the extended ...
Chu, D., Lin, W.-W., Tan, R.C.E.
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Similarity Transformation and Algebraic Riccati Equations

Proceedings of the 45th IEEE Conference on Decision and Control, 2006
In this tutorial paper, a close relationship is established between algebraic Riccati equations and similarity transform. Some results about algebraic Riccati equations are interpreted here using similarity transformations and block diagrams are introduced to represent the stabilising solutions of algebraic Riccati equations.
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On dual algebraic Riccati equations

IEEE Transactions on Automatic Control, 1991
A method is presented to solve dual algebraic Riccati equations. It is shown that only one Schur decomposition of the Hamiltonian matrix is necessary to solve the dual equations. >
L.-F. Wei, F.-B. Yeh
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The algebraic Riccati equation — A polynomial approach

Systems & Control Letters, 1985
This paper considers the problem of classifying the set of all real symmetric solutions of the algebraic Riccati equation (ARE) \(\tilde AX+XA-XB\tilde BX+Q=0\) by using polynomial models, where tilde denotes matrix transpose. For the ARE, we introduce the Hamiltonian \[ H=\left[ \begin{matrix} A&-B\tilde B \\ -Q& -\tilde A\end{matrix} \right] \] and ...
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Note on Perturbation Theory for Algebraic Riccati Equations

SIAM Journal on Matrix Analysis and Applications, 1999
Summary: The expressions for the induced norms of two complex matrix operators, given by \textit{J.-G. Sun} [SIAM J. Matrix Anal. Appl. 19, 39--65 (1998; Zbl 0914.15009)], must be corrected. In this note we give the true values of these induced norms, which are involved in the perturbation analysis of matrix algebraic Riccati equations in the complex ...
Mihail Konstantinov, Petko Hr. Petkov
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The Bezoutian and the algebraic Riccati equation

Linear and Multilinear Algebra, 1984
The classical Bezoutian is a square matrix which counts the common zeros of two polynomials in the complex plane. The usual proofs of this property are based on connections between the Bezoutian and the Sylvester resultant matrix. These proofs do not make transparent the nature of the Bezoutian as a finite dimensional operator.
K. F. Clancey, B. A. Kon
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Sensitivity of algebraic Riccati equations

Proceedings of 35th IEEE Conference on Decision and Control, 2002
The inherent conservatism in standard norm-based bounds for the sensitivity of the continuous-time algebraic Riccati equation is discussed and alternative sensitivity measures are introduced. These measures can be used to model a variety of situations where uncertainty in the data lead to an uncertain solution of the equation, and can be used to ...
T. Gudmundsson, C.S. Kenney, A.J. Laub
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Algebraic Riccati equation and symplectic algebra

International Journal of Control, 1986
Questions of existence, uniqueness and the parametric dependence of solutions of the algebraic Riccati equation are considered. The different criteria for the solubility of this equation are obtained with the help of symplectic algebra.
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On parameter dependence of solutions of algebraic riccati equations

Mathematics of Control, Signals, and Systems, 1988
The paper considers the behaviour of Hermitian solutions, especially the maximal ones (which are obviously unique) of algebraic Riccati equations whose coefficients depend on real parameters. This result is of considerable interest for control theorists.
André C. M. Ran, Leiba Rodman
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