Results 191 to 200 of about 78,251 (234)

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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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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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 bounds of Lyapunov's matrix equation

IEEE Transactions on Automatic Control, 1979
In this paper, new bounds are given for the matrix solution of the Lyapunov equation A'P+ PA+Q=0 . It is shown that it is always possible to achieve a lower bound, while the upper bound can be obtained for a specified class of Q matrices which is given. The results are compared to those given in [1] through some examples.
Geromel, J. C., Bernussou, J.
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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 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 ...
Mori, Takehiro, Fukuma, Norio, Kuwahara, Michiyoshi   +2 more
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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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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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Lyapunov's matrix equation with system matrix in companion form

International Journal of Control, 1993
Abstract A simple method for solving Lyapunov's matrix equation for linear continuous systems with the system matrix in companion form is proposed. The method involves the inversion of the Hurwitz matrix. A necessary and sufficient condition for the existence of a solution to the equation is also obtained.
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Lyapunov and Sylvester Matrix Equations

2013
ADI iterative solution of Lyapunov and Sylvester matrix equations may be enhanced by availability of a stable algorithm for similarity reduction of a full nonsymmetric real matrix to low bandwidth Hessenberg form. An efficient and seemingly stable method described here has been applied successfully to an assortment of test problems.
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