Results 201 to 210 of about 1,640,648 (241)

On the Lyapunov matrix differential equation

IEEE Transactions on Automatic Control, 1986
A lower bound for the determinant of the solution to the Lyapunov matrix differential equation is derived. It is shown that this bound is obtained as a solution to a simple scalar differential equation. In the limiting case where the solution to the Lyapunov differential equation becomes stationary, the result reduces to one of the existing bounds for ...
N Fukuma
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Generalized Lyapunov equation and factorization of matrix polynomials

Systems and Control Letters, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aliev, F. A., Larin, V. B.
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Comments on "On the Lyapunov matrix equation"

IEEE Transactions on Automatic Control, 1975
The Lyapunov matrix equation A'Q + QA = - P is considered in the above paper, where two fundamental inequalities are derived which are satisfied by the extremal eigenvalues of the matrices Q and P provided A is a stability matrix. Similar results are derived by an alternate more simple and straightforward approach using matrix norms.
Montemayor, J. J., Womack, Baxter F.
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Controllability of impulsive matrix Lyapunov systems

Applied Mathematics and Computation, 2015
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Bhaskar Dubey, Raju K. George
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On the Lyapunov matrix equation

IEEE Transactions on Automatic Control, 1974
Given the Lyapunov matrix equation A'Q + QA = -P a fundamental inequality which is satisfied by the extremal eigenvalues of the matrices Q and P , provided A is a stability matrix, is established. This result, besides being interesting from a theoretical standpoint, is extremely useful in the determination of suboptimal controllers for the minimum time
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On the Lyapunov matrix equation

IEEE Transactions on Automatic Control, 1980
In this paper the inequality which is satisfied by the determinant of the solution of the Lyapunov matrix equation A'Q + QA = - D is presented. The result makes possible a lower estimate of product eigenvalues of the matrix Q and dependence from eigenvalues of the matrices A and D .
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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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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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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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