Results 201 to 210 of about 83,867 (245)

The Robust Minkowski–Lyapunov Equation

IEEE Transactions on Automatic Control, 2022
The Lyapunov equation for polytopic linear inclusions over the space of Minkowski functions of nonempty compact and convex sets that contain the origin as an interior point is studied. In particular, necessary and sufficient conditions for the characterization, existence and uniqueness of its fundamental solution are derived.
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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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Solving stiff Lyapunov differential equations

Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
We propose a method based on the matrix generalization of the backward differentiation formula for solving stiff Lyapunov differential equations. This method turns a Lyapunov differential equation into an algebraic Lyapunov equation so that the structure of the original equation can be exploited.
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Multi-Symmetric Lyapunov Equations

IEEE Control Systems Letters, 2023
Xvting Gao, Mario E. Villanueva, Boris Houska   +2 more
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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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Generalized Lyapunov Equations and Positive Definite Functions

SIAM Journal on Matrix Analysis and Applications, 2005
Given a positive definite matrix \(A\), the authors study three types of generalized Lyapunov equations, the first one is \[ A^3X+XA^3+t(A^2 XA+AX A^2)=B. \] the problem in question is whether this equation has a positive semidefinite solution \(X\) whenever \(B\) is positive semidefinite.
Bhatia, Rajendra, Drissi, Driss
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The Sensitivity of the Stable Lyapunov Equation

SIAM Journal on Control and Optimization, 1987
Consider the equation A \(*X+XA=-W\), where A,X,W are \(n\times n\) complex matrices and A is stable (all eigenvalues have negative real parts). No special assumptions about W. For the perturbed equation \((A+\Delta A)\quad *(X+\Delta X)+(X+\Delta X)(A+\Delta A)=-(W+\Delta W)\) the following inequality is proved: \[ \frac{\| \Delta X\|}{\| X+\Delta X\|}
Hewer, Gary, Kenney, Charles
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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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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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Applications of Lyapunov and T-Lyapunov equations in mechanics

2014
This paper considers Lyapunov and T-Lyapunov matrix equations. Lyapunov equation is a matrix equation of the form AX + XA^T = E which plays a vital role in a number of applications, while T-Lyapunov equation is a matrix equation of the form AX +X^TA^T = E.
Kuzmanović Ivičić, Ivana, Truhar, Ninoslav, Tomljanović, Zoran   +2 more
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