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].

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 On the Ψ-asymptotic equivalence of the Ψ-bounded solutions of two Lyapunov matrix differential equations

2020 ◽  
Vol 34 ◽  
pp. 03006
Author(s):  
Aurel Diamandescu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Kronecker Product ◽  
Existence Results ◽  
Bounded Solutions ◽  
Asymptotic Equivalence ◽  
Matrix Differential Equations ◽  
Lyapunov Matrix ◽  
Matrix Differential ◽  
Product Of Matrices

Using Schauder Tychonoff fixed point theorem and the technique of Kronecker product of matrices, we prove existence results for Ψ-asymptotic equivalence of the Ψ-bounded solutions of two Lyapunov matrix differential equations.

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 Stability Analysis of Linear Sylvester System of First Order Differential Equations

2020 ◽  
Vol 9 (11) ◽  
pp. 25252-25259
Author(s):  
Kasi Viswanadh V. Kanuri ◽  
SriRam Bhagavathula ◽  
K.N. Murty
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stability Criteria ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
First Order ◽  
Matrix Differential ◽  
First Order Differential Equations

    In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.

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