Results 221 to 230 of about 14,850 (259)

On the discrete Lyapunov matrix equation

IEEE Transactions on Automatic Control, 1982
Some bounds for the arithmetic and the geometric means of the characteristic roots of the positive semidefinite solution to the discrete Lyapunov matrix equation are derived.
Mori, Takehiro, Fukuma, Norio, Kuwahara, Michiyoshi   +2 more
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One application of Lyapunov’s matrix equation

Journal of Mathematical Sciences, 1998
On the basis of the matrix Lyapunov equation, the property of having fixed sign for an associated quadratic form in the space \(R^{n}\) or in some octant of this space is investigated. A theorem establishing this property is formulated and proved. Also, another theorem determines the conditions which guarantee the property of having fixed sign for the ...
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Analytic perturbation of Sylvester and Lyapunov matrix equations

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002
We consider an analytic perturbation of the Sylvester matrix equation. Mainly we are interested in the singular case, that is, when the null space of the unperturbed Sylvester operator is not trivial, but the perturbed equation has a unique solution. In this case, the solution of the perturbed equation can be given in terms of a Laurent series.
Konstantin E. Avrachenkov, Jean B. Lasserre   +1 more
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Computational experience with the solution of the matrix Lyapunov equation

IEEE Transactions on Automatic Control, 1976
This correspondence presents a comparative study of three methods for the numerical solution of the matrix Lyapunov equation. The test case is a 24th-order system with highly underdamped eigenvalues and a rather high degree of stiffness. The conclusions favor a method by Bartels and Stewart based on a reduction to Schur form of the A matrix.
Belanger, Pierre R., McGillivray, Thomas P.   +1 more
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A New Solution Method for the Lyapunov Matrix Equation

SIAM Journal on Applied Mathematics, 1975
The matrix equation $A^T P + PA = - Q$ is a useful equation for the study of the stability of a system when the dynamics are characterized by $\dot X = AX$. The matrix or system is stable if and only if the solution matrix P is positive definite for a positive definite matrix Q.
Beavers, A. N. jun., Denman, E. D.
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Generalized Lyapunov Equation and Factorization of Matrix Polynomials

IFAC Proceedings Volumes, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aliev, F. A., Larin, V. B.
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Preconditioned Krylov Subspace Methods for Lyapunov Matrix Equations

SIAM Journal on Matrix Analysis and Applications, 1995
The authors are concerned with the iterative solution of the following Lyapunov matrix equations \(AX + XA^T = -D^T D\) by preconditioned Krylov subspace methods. Instead of working with Krylov subspaces associated with the matrix \(A\), they interpret the Lyapunov equation as a linear system with the coefficient matrix given by the Kronecker sum \(A ...
Starke, Gerhard, Hochbruck, Marlis
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Lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations

Automatica, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han Ho Choi, Tae-Yong Kuc
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A theorem on the Lyapunov matrix equation

IEEE Transactions on Automatic Control, 1969
Given the Lyapunov matrix equation A'P + PA + 2\sigmaQ = 0 where σ is some positive scalar, a necessary and sufficient condition for the real parts of the eigenvalues of A to be less than -σ is that P - Q is negative definite. The condition provides an upper bound to the solution of the Lyapunov matrix equation and is useful in the design of minimum ...
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Solution of the Lyapunov matrix equation for a system with a time‐dependent stiffness matrix

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2003
AbstractThe stability of the linearized model of a rotor system with non‐symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces.
Pommer, Christian, Kliem, Wolfhard
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