Results 181 to 190 of about 135,095 (252)

Nonsymmetric algebraic Riccati equations

2011
The research activity concerning the analysis of nonsymmetric algebraic Riccati equations associated with M-matrices and the design of numerical algorithms for their solution has had a strong acceleration in the last decade. Important progresses have been obtained concerning theoretical properties of this class of matrix equations and new effective ...
openaire   +1 more source

The symmetric algebraic Riccati equation

2010
As we know from the previous part there is an intimate connection between canonical factorization and Riccati equations. In this chapter this connection is developed further for the case when the rational matrix functions involved have Hermitian values on the imaginary axis.
Harm Bart, Marinus A. Kaashoek, André C. M. Ran   +2 more
openaire   +1 more source

The Algebraic Riccati Equation without Complete Controllability

SIAM Journal on Algebraic Discrete Methods, 1982
The equation $XDX + XA + A^*X - C = 0$ is studied under the assumptions that D is positive semidefinite and to pure imaginary eigenvalues of the Hamiltonian matrix $\begin{pmatrix} A & D \\ C & { - A^* } \end{pmatrix}$ correspond only elementary divisors of even degree.
openaire   +1 more source

Approximate Stabilizability via the Algebraic Riccati Equation

SIAM Journal on Control and Optimization, 1985
The problem considered is the stabilizability of an infinite dimensional linear system on a Hilbert space by means of state feedback. The feedback gain operator is the solution of an algebraic Riccati equation related to the system. For infinite dimensional systems one can prove only a weaker type of stabilizability: the closed-loop system is only ...
openaire   +2 more sources

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 ...
openaire   +2 more sources

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 ...
openaire   +3 more sources

Non-Hermitian Solutions of Algebraic Riccati Equations

Canadian Journal of Mathematics, 1997
AbstractNon-hermitian solutions of algebraic matrix Riccati equations (of the continuous and discrete types) are studied. Existence is proved of non-hermitian solutions with given upper bounds of the ranks of the skew-hermitian parts, under the sign controllability hypothesis.
openaire   +1 more source

Closed-form solution of non-symmetric algebraic Riccati matrix equation

Applied Mathematics Letters, 2022
Akbar Shirilord, M. Dehghan
semanticscholar   +1 more source

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 ...
openaire   +2 more sources

Stabilizing Solution and Parameter Dependence of Modified Algebraic Riccati Equation With Application to Discrete-Time Network Synchronization

IEEE Transactions on Automatic Control, 2016
Michael Z. Q. Chen, Liangyin Zhang, Housheng Su, Guanrong Chen   +3 more
semanticscholar   +1 more source