scholarly journals A Necessary and Sufficient Condition for the Asymptotic Stability of the Damped Oscillator

1995 ◽  
Vol 119 (1) ◽  
pp. 209-223 ◽  
Author(s):  
L. Hatvani ◽  
T. Krisztin ◽  
V. Totik
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Damped Oscillator

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

1976 ◽  
Vol 74 ◽  
pp. 71-79
Author(s):  
R. Datko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Linear Ordinary Differential Equations ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

scholarly journals Lyapunov-Krasovskii stability analysis of nonlinear integro-differential equation

2018 ◽  
Vol 7 (2) ◽  
pp. 53
Author(s):  
Prebo Jackreece
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Integro Differential Equation ◽  
Necessary And Sufficient

The purpose of this paper is to develop a qualitative stability analysis of a class of nonlinear integro-differential equation within the framework of Lyapunov-Krasovskii. We show that the existence of a Lyapunov-Krasovskii functional is a necessary and sufficient condition for the uniform asymptotic stability of the nonlinear Volterra integro-differential equations.

A Simple Alternative to the Routh-Hurwitz Criterion for Symmetric Systems

1970 ◽  
Vol 37 (4) ◽  
pp. 1168-1170 ◽  
Author(s):  
T. J. Moran
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Necessary And Sufficient Condition ◽  
Principal Coordinates ◽  
Simple Alternative ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Gyroscopic Systems ◽  
Symmetric Systems

A necessary and sufficient condition for the asymptotic stability of damped, linear, symmetric, multidegree of freedon systems is given. The condition is easily applied if the principal coordinates for the undamped system are known. The stability properties of such systems which are not asymptotically stable are investigated and the result is extended to gyroscopic systems.

scholarly journals Multidimensional Tauberian theorems for vector-valued distributions

2014 ◽  
Vol 95 (109) ◽  
pp. 1-28 ◽  
Author(s):  
Stevan Pilipovic ◽  
Jasson Vindas
Keyword(s):  
Asymptotic Stability ◽  
Integral Transform ◽  
Tauberian Theorems ◽  
Sufficient Condition ◽  
Cauchy Problems ◽  
Necessary And Sufficient Condition ◽  
The Laplace Transform ◽  
Distribution Spaces ◽  
Necessary And Sufficient ◽  
Vector Valued

We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of f is given by the integral transform Mf?(x,y) = (f*?y)(x), (x,y) ? Rn ? R+, with kernel ?y(t) = y?n?(t/y). We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quasiasymptotics in distribution spaces, and we give a necessary and sufficient condition for the existence of the trace of a distribution on {x0}?Rm. In addition, we present a new proof of Littlewood?s Tauberian theorem.

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