New stability conditions for linear difference equations using Bohl-Perron type theorems

Leonid Berezansky; Elena Braverman

doi:10.1080/10236190903146938

New stability conditions for linear difference equations using Bohl-Perron type theorems

Leonid Berezansky, Elena Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.

Original language	English
Pages (from-to)	657-675
Number of pages	19
Journal	Journal of Difference Equations and Applications
Volume	17
Issue number	5
DOIs	https://doi.org/10.1080/10236190903146938
State	Published - 1 May 2011

Keywords

Exponential stability
Linear delay difference equations
Positive fundamental function

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236190903146938

Cite this

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title = "New stability conditions for linear difference equations using Bohl-Perron type theorems",

abstract = "The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.",

keywords = "Exponential stability, Linear delay difference equations, Positive fundamental function",

author = "Leonid Berezansky and Elena Braverman",

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N2 - The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.

AB - The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.

KW - Exponential stability

KW - Linear delay difference equations

KW - Positive fundamental function

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JF - Journal of Difference Equations and Applications

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New stability conditions for linear difference equations using Bohl-Perron type theorems

Abstract

Keywords

ASJC Scopus subject areas

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