Results 191 to 200 of about 1,417,876 (221)

The Algebraic Matrix Riccati Equation

1984
We review some recent results concerning the symmetric algebraic matrix Riccati equation and especially its hermitian solutions. The main idea is description of such solutions in terms of invariant subspaces of a certain matrix, which is self-adjoint in an indefinite scalar product. Some new results on this subject are presented as well.
A. C. M. Ran, L. Rodman
openaire   +1 more source

The shift techniques for a nonsymmetric algebraic Riccati equation

Applied Mathematics and Computation, 2013
In this paper, we want to analyze a special instance of a nonsymmetric algebraic matrix Riccati equation arising from transport theory. Traditional approaches for finding its minimal nonnegative solution are based on fixed point iterations and the speed of the convergence is linear.
Matthew M. Lin, Chun-Yueh Chiang
openaire   +2 more sources

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

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 Algebraic Riccati Equation (ARE)

2018
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Geometry of the algebraic Riccati equation. I

The algebraic Riccati equation (ARE) is the matrix equation \(-A'K- KA+KBB'K-Q=0,\) where A, B, Q are real matrices and Q is symmetric. Its solutions are equilibrium points of the Riccati differential equation of linear quadratic control. Two well-known methods are available for studying the ARE: the ''Hamiltonian matrix method'' associates to every ...
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Closed-form solution of non-symmetric algebraic Riccati matrix equation

Applied Mathematics Letters, 2022
Mehdi Dehghan, Akbar Shirilord
exaly  

Geometry of the Algebraic Riccati Equation, Part II

SIAM Journal on Control and Optimization, 1983
Mark A Shayman
exaly  

Geometry of the Algebraic Riccati Equation, Part I

SIAM Journal on Control and Optimization, 1983
Mark A Shayman
exaly  

Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation

IEEE Transactions on Automatic Control, 1986
Sheng-De Wang, Te-Son Kuo, Chen-Fa Hsu   +2 more
exaly