$\Psi$-bounded solutions for a Lyapunov matrix differential equation [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2009 It is proved a necessary and sufficient condition for the existence of at least one $\Psi$-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation.
Aurel Diamandescu
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On $\Psi$-stability of nonlinear Lyapunov matrix differential equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We prove necessary and sufficient conditions for $\Psi -$ (uniform) stability of the trivial solution of a nonlinear Lyapunov matrix differential equation.
Aurel Diamandescu
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Annals of the West University of Timisoara: Mathematics and Computer Science, 2022 The aim of this paper is to give sufficient conditions for Ψ − conditional exponential asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
Diamandescu Aurel
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Existence of $\Psi$-bounded solutions for nonhomogeneous Lyapunov matrix differential equations on $R$ [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2010 In this paper, we give a necessary and sufficient condition for the existence of at least one $\Psi$-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation on $\mathbb{R}$.
Aurel Diamandescu
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Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation
Mathematics, 2021 Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition.
Vera Angelova +2 more
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New estimates for the solution of the Lyapunov matrix differential equation [PDF]
The Electronic Journal of Linear Algebra, 2010 In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation.
Juan Zhang, Jianzhou Liu
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Existence of Ψ Bounded Solutions for a Lyapunov Matrix Dierential Equation
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 It is proved a necessary and sufficient condition for the existence of at least one Ψ- bounded solution of a linear non- homogeneous Lyapunov matrix differential equation.
Diamandescu Aurel
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On ψ Bounded Solutions for a Nonlinear Lyapunov Matrix Differential Equation on [PDF]
Annals of the West University of Timisoara: Mathematics and Computer Science, 2018 Using Banach and Schauder - Tychono fixed point theorems, existence results for a nonlinear Lyapunov matrix differential equation on are given. The obtained results generalize and extend the results from [5] and [18].
Diamandescu Aurel
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The eigenvalue product bounds of the Lyapunov matrix differential equation and the stability of a class of time-varying nonlinear system [PDF]
Journal of Inequalities and Applications, 2019 The Lyapunov matrix differential equation plays an important role in many scientific and engineering fields. In this paper, we first give a class relation between the eigenvalue of functional matrix derivative and the derivative of functional matrix ...
Jianzhou Liu, Juan Zhang, Hao Huang
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On the Ψ-Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations [PDF]
Annals of the West University of Timisoara: Mathematics and Computer Science, 2015 It is proved (necessary and) sufficient conditions for Ψ − conditional asymptotic stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations.
Diamandescu Aurel
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