Excitation Conditions for Uniform Exponential Stability of the Cooperative Gradient Algorithm over Weakly Connected Digraphs

2021 ◽  
pp. 1-1
Author(s):  
Muhammad U. Javed ◽  
Jorge I. Poveda ◽  
Xudong Chen
Keyword(s):  
Exponential Stability ◽  
Gradient Algorithm ◽  
Uniform Exponential Stability ◽  
Excitation Conditions

The uniform exponential stability of a class of linear differential–difference equations in a Hilbert space

1981 ◽  
Vol 89 (3-4) ◽  
pp. 201-215 ◽  
Author(s):  
Richard Datko
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Exponential Stability ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Exponential Stability ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is given for the uniform exponential stability of certain autonomous differential–difference equations whose phase space is a Hilbert space. It is shown that this property is preserved when the delays depend homogeneously on a nonnegative parameter.

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