Results 171 to 180 of about 1,417,876 (221)
Some of the next articles are maybe not open access.
The Algebraic Riccati Equation for Quaternions
Advances in Applied Clifford Algebras, 2013The paper studies a Riccati equation \[ p(x):=a+bx+xc+xdx=0,\qquad a,b,c,d,x \in \mathbb{H}, \] where \(p\) is a quaternionic polynomial, which is shown to be reducible to a one-sided type. The set of quaternions \( \mathbb{H}\) can be seen as the four-dimensional vector space \( \mathbb{R}^4\) equipped with a special multiplication rule.
Janovská, Drahoslava, Opfer, Gerhard
openaire +2 more sources
1995
Abstract This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions.
Peter Lancaster, Leiba Rodman
openaire +1 more source
Abstract This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions.
Peter Lancaster, Leiba Rodman
openaire +1 more source
On the Algebraic Riccati Equations of Finite Elastostatics
Journal of Elasticity, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
The Riccati algebraic equation in a locallyC ⋆-algebra
Integral Equations and Operator Theory, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
On the solvability of the Riccati matrix algebraic equation [PDF]
Ukrainian Mathematical Journal, 1994 Одержано деякі умови розв’язності матричного алгебраїчного рівняння Ріккаїі.We obtain conditions of solvability of the Riccati matrix algebraic ...
Прокіп, В.М.
exaly +2 more sources
Perturbation Theory for Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications, 1998The 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.
openaire +3 more sources
On the discrete-time algebraic Riccati equation
Proceedings of the 1972 IEEE Conference on Decision and Control and 11th Symposium on Adaptive Processes, 1972A 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.
openaire +2 more sources
Riccati Equations on Noncommutative Banach Algebras
SIAM Journal on Control and Optimization, 2011Conditions 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 ...
openaire +2 more sources
The Dissipation Inequality and the Algebraic Riccati Equation
1991Undoubtedly 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.
openaire +2 more sources
Equivalence Relations for the Algebraic Riccati Equation
SIAM Journal on Control, 1973By 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 ...
openaire +3 more sources