A note on the nonuniform exponential stability and dichotomy for nonautonomous difference equations

2018 ◽  
Vol 552 ◽  
pp. 105-126 ◽  
Author(s):  
Davor Dragičević
Keyword(s):  
Exponential Stability ◽  
Difference Equations ◽  
Nonuniform Exponential Stability

scholarly journals A New Approach on Datko–Zabczyk Method for Nonuniform Exponential Stability

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1095
Author(s):  
Nicolae Lupa
Keyword(s):  
Exponential Stability ◽  
Large Class ◽  
Linear Space ◽  
Difference Equations ◽  
Discrete Dynamics ◽  
New Approach ◽  
Banach Sequence Spaces ◽  
Nonuniform Exponential Stability ◽  
Banach Sequence

We provide a sequence of projections on the linear space of all sequences and connect the existence of nonuniform exponential stability to the restrictions of these projections on a class of Banach sequence spaces defined by a discrete dynamics. As a consequence, we obtain a Datko–Zabczyk type characterization of nonuniform exponential stability. We develop our analysis without any assumption on the invertibility of the dynamics, thus our results are applicable to a large class of difference equations.

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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