Results 161 to 170 of about 14,195 (209)

Perturbation Theory for Algebraic Riccati Equations

SIAM Journal on Matrix Analysis and Applications, 1998
The continuous-time algebraic Riccati equation (CARE) \[ Q+A^HX+XA-XGX=0 \] and the discrete-time algebraic Riccati equation (DARE) \[ X-A^HX(I+GX)^{-1}A-Q=0 \] are considered. Appropriate assumptions on the coefficient matrices are made to guarantee the existence and uniqueness of a Hermitian positive semidefinite (p.s.d.) solution.
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The Dissipation Inequality and the Algebraic Riccati Equation

1991
Undoubtedly one of the most important concepts in linear systems and control, both from a theoretical as well as from a practical point of view, is the algebraic Riccati equation. Since its introduction in control theory by Kaiman [16] the beginning of the sixties, the algebraic Riccati equation has known an impressive range of applications, such as ...
Trentelman, Hendrikus, Willems, Jan C.
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On the discrete-time algebraic Riccati equation

Proceedings of the 1972 IEEE Conference on Decision and Control and 11th Symposium on Adaptive Processes, 1972
A detailed account of the properties of a class of algebraic Riccati equations which arise in discrete time control and filtering problems is given. It is shown that a generalized notion of detectability plays an important role in classifying solutions of these equations. This concept is also related to a minimum phase condition.
Payne, Harold J., Silverman, Leonard M.
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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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Riccati Equations on Noncommutative Banach Algebras

SIAM Journal on Control and Optimization, 2011
Conditions for the existence of a solution of a Riccati equation to be in some prescribed noncommutative involutive Banach algebras are given. The Banach algebras are inverse-closed subalgebras of the space of bounded linear operators on some Hilbert space, and the Riccati equation has an exponentially stabilizing solution on this larger space ...
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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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An Algorithm for Solving a Perturbed Algebraic Riccati Equation

European Journal of Control, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo F. Costa, João B. R. do Val
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Equivalence Relations for the Algebraic Riccati Equation

SIAM Journal on Control, 1973
By generalizing the notion of spectral factorization, solutions X of the matrix quadratic equation $BX + XA - XCDX + Q = 0$ are shown to have a one-to-one relation with factorizations of a rational matrix. By progressive specialization of this factorization, equivalence results are obtained in turn for symmetric solutions, Hermitian solutions ...
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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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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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