Lower Eigenvalue Bounds on Summation for the Solution of the Lyapunov Matrix Differential Equation

2016 ◽  
Vol 19 (1) ◽  
pp. 382-390
Author(s):  
Juan Zhang ◽  
Jianzhou Liu ◽  
Hao Huang
Keyword(s):  
Differential Equation ◽  
Lower Eigenvalue ◽  
Matrix Differential Equation ◽  
Eigenvalue Bounds ◽  
Lyapunov Matrix ◽  
Matrix Differential

scholarly journals Existence of Ψ Bounded Solutions for a Lyapunov Matrix Dierential Equation

2014 ◽  
Vol 52 (2) ◽  
Author(s):  
Aurel Diamandescu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Bounded Solution ◽  
Sufficient Condition ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Lyapunov Matrix ◽  
Matrix Differential ◽  
Necessary And Sufficient

AbstractIt 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. In addition, it is given a result in connection with the asymptotic behavior of the Ψ- bounded solutions of this equation.

scholarly journals Note on the existence of a Ψ-bounded solution for a Lyapunov matrix differential equation

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Aurel Diamandescu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Bounded Solution ◽  
Sufficient Condition ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Lyapunov Matrix ◽  
Matrix Differential ◽  
Necessary And Sufficient

AbstractIn this paper, we give a necessary and sufficient condition for the existence of at least one Ψ-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation. In addition, we give a result in connection with the asymptotic behavior of the Ψ-bounded solutions of this equation.

scholarly journals On ψ Bounded Solutions for a Nonlinear Lyapunov Matrix Differential Equation on 𝕉

2018 ◽  
Vol 56 (2) ◽  
pp. 131-150
Author(s):  
Aurel Diamandescu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
Lyapunov Matrix ◽  
Matrix Differential

AbstractUsing 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].

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