Results 211 to 220 of about 1,640,648 (241)

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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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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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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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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An explicit solution to the generalized Lyapunov matrix inequality

Systems & Control Letters
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Mario Spirito, Daniele Astolfi
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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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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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On the hyper-Lyapunov matrix inclusions

Linear Algebra and its Applications
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Some Applications of the Lyapunov Matrix Equation

IMA Journal of Applied Mathematics, 1968
Barnett, S., Storey, C.
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