Sufficient conditions for the stability of solutions of a linear differential system of second order

1981 ◽  
Vol 32 (3) ◽  
pp. 268-273
Author(s):  
G. A. Los'
Keyword(s):  
Differential System ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential System ◽  
Stability Of Solutions ◽  
Linear Differential ◽  
The Stability

scholarly journals Note on a Resolution of Linear Differential Systems

1934 ◽  
Vol 4 (1) ◽  
pp. 36-40
Author(s):  
I. S. ◽  
E. S. Sokolnikoff
Keyword(s):  
Differential System ◽  
Lower Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Differential System ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Equivalent Systems ◽  
Linear Differential ◽  
Necessary And Sufficient

In a recent paper J. M. Whittaker considered the problem of resolving a linear differential system into a product of two or more systems of lower order. This note is a contribution to this problem and furnishes the necessary and sufficient conditions for the resolution of the system into two equivalent systems of lower order of the type considered by Whittaker.

scholarly journals Stability of a Functional Differential System with a Finite Number of Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Rebenda ◽  
Zdeněk Šmarda
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Stability Of Solutions ◽  
Functional Differential ◽  
The Stability ◽  
Complex Valued ◽  
Functional Differential System

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.

On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation

2020 ◽  
Vol 17 (2) ◽  
pp. 188-195
Author(s):  
Samandar Iskandarov ◽  
Nazigai Abdiraiimova
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Linear Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Stability Of Solutions ◽  
Volterra Type ◽  
Order Linear ◽  
Linear Differential

Sufficient conditions for the asymptotic stability of the solutions of a second-order linear integro-differential equation of the Volterra type are established in the case where the solutions of the corresponding second-order linear differential equation may have no property under study. Thus, the influence of integral perturbations on the asymptotic stability of solutions of linear differential equations of the second order is revealed. For this purpose, the method of auxiliary kernels is developed. An illustrative example is given.

scholarly journals STABILITY OF ZERO SOLUTION OF SYSTEM WITH SWITCHES CONSISTING OF LINEAR SUBSYSTEMS

2020 ◽  
pp. 89-96
Author(s):  
D. Khusainov ◽  
A. Bychkov ◽  
A. Sirenko
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Switching Systems ◽  
Stability Of Solutions ◽  
Quadratic Lyapunov Function ◽  
Linear Differential ◽  
The Stability

In this paper, discusses the study of the stability of solutions of dynamic systems with switching. Sufficient conditions are obtained for the asymptotic stability of the zero solution of switching systems consisting of linear differential and difference subsystems. It is proved that the existence of a common quadratic Lyapunov function is sufficient for asymptotic stability.

An Asymptotical Stability in Variational Sense for Second Order Systems

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Dariusz Idczak ◽  
Stanisław Walczak
Keyword(s):  
Sobolev Space ◽  
Differential System ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Second Order ◽  
Functional Parameter ◽  
Asymptotical Stability ◽  
Parameter Control ◽  
Initial Condition ◽  
Second Order Systems

AbstractIn this paper, a new, variational concept of asymptotical stability of zero solution to an ordinary differential system of the second order, considered in Sobolev space, is presented. Sufficient conditions for an asymptotical stability in a variational sense with respect to initial condition and functional parameter (control) are given. Relation to the classical asymptotical stability is illustrated.

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

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